Fixed abrasive articles and methods of forming same

ABSTRACT

A fixed abrasive article having a body including abrasive particles contained within a bond material, the abrasive particles including shaped abrasive particles or elongated abrasive particles having an aspect ratio of length:width of at least 1.1:1, each of the shaped abrasive particles or elongated abrasive particles having a predetermined position or a predetermined three-axis orientation.

CROSS-REFERENCE TO RELATED APPLICATION(S)

The present application is a continuation of U.S. patent applicationSer. No. 16/448,317, filed Jun. 21, 2019, entitled “Fixed AbrasiveArticles and Methods of Forming Same,” naming inventors Adam P.BUJNOWSKI et al., which is a continuation of U.S. patent applicationSer. No. 15/905,023, filed Feb. 26, 2018, entitled “Fixed AbrasiveArticles and Methods of Forming Same,” naming inventors Adam P.BUJNOWSKI et al., now U.S. Pat. No. 10,358,589, which is a continuationof U.S. patent application Ser. No. 15/087,715, filed Mar. 31, 2016,entitled “Fixed Abrasive Articles and Methods of Forming Same,” naminginventors Adam P. BUJNOWSKI et al., now U.S. Pat. No. 9,938,440, whichclaims priority to U.S. Provisional Application No. 62/289,518, filedFeb. 1, 2016, entitled “Fixed Abrasive Articles and Methods of FormingSame,” naming inventors Adam P. BUJNOWSKI et al., U.S. ProvisionalApplication No. 62/259,509, filed Nov. 24, 2015, entitled “FixedAbrasive Articles and Methods of Forming Same,” naming inventors Adam P.BUJNOWSKI et al., and U.S. Provisional Application No. 62/141,166, filedMar. 31, 2015, entitled “Fixed Abrasive Articles and Methods of FormingSame,” naming inventors Adam P. BUJNOWSKI et al., all of which areassigned to the current assignees hereof and incorporated herein byreference in their entireties.

BACKGROUND Field of the Disclosure

The following is directed to fixed abrasive articles, and moreparticularly, to fixed abrasive articles including shaped abrasiveparticles or elongated abrasive particles.

Description of the Related Art

Abrasive articles incorporating abrasive particles are useful forvarious material removal operations including grinding, finishing,polishing, and the like. Depending upon the type of abrasive material,such abrasive particles can be useful in shaping or grinding variousmaterials in the manufacturing of goods. Certain types of abrasiveparticles have been formulated to date that have particular geometries,such as triangular shaped abrasive particles and abrasive articlesincorporating such objects. See, for example, U.S. Pat. Nos. 5,201,916;5,366,523; and 5,984,988.

Previously, three basic technologies that have been employed to produceabrasive particles having a specified shape are fusion, sintering, andchemical ceramic. In the fusion process, abrasive particles can beshaped by a chill roll, the face of which may or may not be engraved, amold into which molten material is poured, or a heat sink materialimmersed in an aluminum oxide melt. See, for example, U.S. Pat. No.3,377,660. In sintering processes, abrasive particles can be formed fromrefractory powders having a particle size of up to 10 micrometers indiameter. Binders can be added to the powders along with a lubricant anda suitable solvent to form a mixture that can be shaped into plateletsor rods of various lengths and diameters. See, for example, U.S. Pat.No. 3,079,242. Chemical ceramic technology involves converting acolloidal dispersion or hydrosol (sometimes called a sol) to a gel orany other physical state that restrains the mobility of the components,drying, and firing to obtain a ceramic material. See, for example, U.S.Pat. Nos. 4,744,802 and 4,848,041.

The industry continues to demand improved abrasive materials andabrasive articles.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure may be better understood, and its numerousfeatures and advantages made apparent to those skilled in the art byreferencing the accompanying drawings.

FIG. 1 includes a perspective view illustration of a fixed abrasivearticle according to an embodiment.

FIG. 2 includes a perspective view illustration of a shaped abrasiveparticle according to an embodiment.

FIG. 3A includes a perspective view illustration of a shaped abrasiveparticle in accordance with an embodiment.

FIG. 3B includes a perspective view illustration of an elongatedabrasive particle according to an embodiment.

FIG. 4A includes an illustration of a shaped abrasive particle accordingto an embodiment.

FIG. 4B includes an illustration of a shaped abrasive particle inaccordance with an embodiment.

FIG. 4C includes an illustration of a shaped abrasive particle inaccordance with an embodiment.

FIG. 4D includes an illustration of a shaped abrasive particle inaccordance with an embodiment.

FIG. 5A includes an illustration of a portion of a fixed abrasivearticle including abrasive particles in accordance with an embodiment.

FIG. 5B includes an illustration of abrasive particles within a fixedabrasive article in accordance with an embodiment.

FIG. 5C includes an illustration of a plurality of abrasive particleswithin a fixed abrasive article according to an embodiment.

FIG. 6 includes an illustration of a portion of a fixed abrasive articleincluding abrasive particles in accordance with an embodiment.

FIG. 7 includes an illustration of a portion of a fixed abrasive articleincluding abrasive particles in accordance with an embodiment.

FIG. 8 includes an illustration of a portion of a fixed abrasive articleincluding abrasive particles in accordance with an embodiment.

FIG. 9 includes a flowchart illustrating a method of forming a fixedabrasive article in accordance with an embodiment.

FIGS. 10A-10C include illustrations of a system for forming a fixedabrasive article in accordance with an embodiment.

FIG. 11 includes an illustration of a system for forming a fixedabrasive article in accordance with an embodiment.

FIG. 12A includes an illustration of a system for forming a fixedabrasive article in accordance with an embodiment.

FIG. 12B includes an illustration of a forming structure for forming afixed abrasive article in accordance with an embodiment.

FIG. 13 includes an illustration of a system for forming a fixedabrasive article in accordance with an embodiment.

FIGS. 14A and 14B include illustrations of systems for forming a fixedabrasive article in accordance with an embodiment.

FIG. 14C includes an image of a production tool used to form a fixedabrasive article according to an embodiment.

FIG. 14D includes an image of a production tool used to form a fixedabrasive article according to an embodiment.

FIG. 15 includes a flowchart illustrating a method of forming a fixedabrasive article in accordance with an embodiment.

FIG. 16 includes an illustration of a system for forming a fixedabrasive article in accordance with an embodiment.

FIGS. 17A and 17B include illustrations of a system for forming a fixedabrasive article in accordance with an embodiment.

FIG. 18 includes an illustration of a system for forming a fixedabrasive article in accordance with an embodiment.

FIG. 19 includes an illustration of a system for forming a fixedabrasive article in accordance with an embodiment.

FIG. 20A includes a top-down illustration of a portion of an abrasivearticle in accordance with an embodiment.

FIGS. 20B-20D include illustrations of distributions in accordance withan embodiment.

FIG. 21 includes a top-down illustration of a portion of an abrasivearticle in accordance with an embodiment.

DETAILED DESCRIPTION

In accordance with an embodiment a fixed abrasive article is disclosed.The fixed abrasive article may be suitable for material removaloperations on a variety of workpieces including for example metal ormetal alloy materials. Moreover, in certain instances, the fixedabrasive articles of the embodiments herein can include bonded abrasivearticles, and more particularly, roll grinding bonded abrasive wheels,flexible thin wheels, and the like. Such products may be particularlysuitable for material removal operations including for example, traversegrinding, angle grinding, and the like.

FIG. 1 includes a perspective view illustration of a fixed abrasivearticle in accordance with an embodiment. As illustrated, the fixedabrasive article 100 can have a body 101 of a generally cylindricalshape including an upper surface 102, a bottom surface 104, and a sidesurface 103 extending between the upper surface 102 and bottom surface104. It will be appreciated that the fixed abrasive article of FIG. 1 isa non-limiting example, and other shapes of the body may be utilizedincluding, but not limited to, conical, cup-shaped, depressed centerwheels (e.g., T42), and the like. Finally, as further illustrated, thebody 101 can include a central opening 185 which may be configured toaccept an arbor or shaft for mounting of the body 101 on a machineconfigured to rotate the body 101 and facilitate a material removaloperation.

The fixed abrasive article 100 can have a body 101 including abrasiveparticles, including for example, the groups of abrasive particles 105and 106, contained within the volume of the body 101. The abrasiveparticles may be contained within the three-dimensional volume of thebody 101 by a bond material 107 that can extend throughout thethree-dimensional volume of the body 101. In accordance with anembodiment, the bond material 107 can include materials such asvitreous, polycrystalline, monocrystalline, organic (e.g., resin),metal, metal alloys, and a combination thereof.

In a particular embodiment, the abrasive particles may be encapsulatedwithin the bond material 107. As used herein, “encapsulated” refers to acondition whereby at least one of the abrasive particles is fullysurrounded by a homogenous, or generally homogenous, composition of bondmaterial. In an embodiment, an abrasive particle encapsulated within abond material may be fully surrounded by a homogenous composition. Moreparticularly, the encapsulated abrasive particle may be fully surroundedby a composition essentially free of discernable strati associated with,for example, layering. In a particular embodiment, a majority of theabrasive particles can be encapsulated within the bond material 107. Ina more particular embodiment, all of the abrasive particles can beencapsulated within the bond material 107.

In accordance with an embodiment, at least 1% of the abrasive particlescan be encapsulated within the bond material 107. In a more particularembodiment, at least 5% of the abrasive particles can be encapsulatedwithin the bond material 107, at least 10% of the abrasive particles canbe encapsulated within the bond material 107, at least 25% of theabrasive particles can be encapsulated within the bond material 107, atleast 50% of the abrasive particles can be encapsulated within the bondmaterial 107, at least 75% of the abrasive particles can be encapsulatedwithin the bond material 107, at least 90% of the abrasive particles canbe encapsulated within the bond material 107, or even at least 95% ofthe abrasive particles can be encapsulated within the bond material 107.In a further embodiment, 100% of the abrasive particles can beencapsulated within the bond material 107.

In an embodiment, the fixed abrasive article 100 can be essentially freeof a fixation layer. In a particular instance, the fixed abrasivearticle 100 can be substantially uniform throughout a volume of the body101. In more particular instances, the body 101 can have a substantiallyhomogenous composition throughout the volume of the body 101.

In accordance with an embodiment, the abrasive particles containedwithin the fixed abrasive 100 can include abrasive materials including,but not limited to, oxides, carbides, nitrides, borides, oxycarbides,oxynitrides, oxyborides, superabrasives, diamond, cubic boron nitride,carbon-containing materials, and any combination thereof. In moreparticular instances, the abrasive particles may include amonocrystalline material, a polycrystalline material, a vitreousmaterial, and any combination thereof. In at least one embodiment, theabrasive particles can include a material such as alumina, zirconia,magnesia, rare-earth oxides, and a combination thereof.

Moreover, the fixed abrasive article 100 can include a combination ofabrasive particles, including one or more types of abrasive particles,such as primary and secondary types of abrasive particles. Primary andsecondary types may refer to the content of the abrasive particleswithin the body of the fixed abrasive article, wherein the primary typeof abrasive particles are present in a higher content than the secondarytype of abrasive particles. In other instances, the distinction betweenprimary and secondary types of abrasive particles may be based upon theposition of the abrasive particle within the body, wherein the primaryabrasive particles may be positioned to conduct an initial stage ofmaterial removal or conduct the majority of material removal compared tothe secondary abrasive particles. In still other instances, thedistinction between primary and secondary abrasive particles may pertainto the abrasive nature (e.g., hardness, friability, fracture mechanics,etc.) of the abrasive particles, wherein the abrasive nature of theprimary particles is typically more robust as compared to the secondarytype of abrasive particles. Some suitable examples of abrasive particlesthat may be considered as a secondary type of abrasive particle includediluent particles, agglomerated particles, unagglomerated particles,naturally occurring materials (e.g., minerals), synthetic materials, anda combination thereof.

In certain instances, the fixed abrasive article 100 can include aparticular content of abrasive particles within the body 101 that mayfacilitate suitable material removal operations. For example, the body101 can include a content of abrasive particles of at least 0.5 vol %for a total volume of the body 101. In other instances, the content ofabrasive particles within the body 101 may be greater, such as at least1 vol %, at least 5 vol %, at least 10 vol %, at least 15 vol %, atleast 20 vol %, at least 25 vol %, at least 30 vol %, at least 35 vol %,at least 40 vol %, or even at least 45 vol %. Still, in anothernon-limiting embodiment, the content of abrasive particles within thebody 101 can be not greater than 60 vol %, such as not greater than 55vol %, not greater than 50 vol %, not greater than 45 vol %, not greaterthan 40 vol %, not greater than 35 vol %, not greater than 30 vol %, notgreater than 25 vol %, not greater than 20 vol %, not greater than 15vol %, or even not greater than 10 vol %. It will be appreciated thatthe content of abrasive particles within the body 101 can be within arange including any of the minimum and maximum percentages noted aboveincluding, but not limited to, at least 0.5 vol % to not greater than 50vol %, such as at least 1 vol % and not greater than 45 vol %, or evenwithin a range of at least 5 vol % and not greater than 40 vol %.

Furthermore, the body 101 of the fixed abrasive article 100 can includea particular content of bond material 107 that may facilitate suitableoperation of the fixed abrasive article 100. For example, the body 101can include a content of bond material 107 of at least 0.5 vol % for atotal volume of the body 101. In other embodiments, the content of bondmaterial 107 can be greater, such as at least 1 vol %, at least 5 vol %,at least 10 vol %, at least 20 vol %, at least 30 vol %, at least 40 vol%, at least 50 vol %, at least 60 vol %, or even at least 70 vol %.Still, in a non-limiting embodiment, the body 101 can have a content ofbond material 107 of not greater than about 90 vol %, such as notgreater than 80 vol %, not greater than 70 vol %, not greater than 60vol %, not greater than 50 vol %, not greater than 40 vol %, not greaterthan 30 vol %, not greater than 20 vol %, or even not greater than 10vol %. It will be appreciated that the content of bond material 107within the body 101 can be within a range including any of the minimumand maximum percentages noted above, including for example within arange including at least 0.5 vol % and not greater than 80 vol %, with arange of at least 0.5 vol % and not greater than 50 vol %, or even witha range of at least 1 vol % to not greater than 40 vol %.

In certain instances, the fixed abrasive article can have a body 101including a content of porosity. The porosity can extend throughout atleast a portion of the entire volume of the body 101, and in certaininstances, may extend substantially uniformly throughout the entirevolume of the body 101. For example, the porosity can include closedporosity or open porosity. Closed porosity can be in the form ofdiscrete pores that are isolated from each other by bond material and/orabrasive particles. Such closed porosity may be formed by pore formers.In other instances, the porosity may be open porosity defining aninterconnected network of channels extending throughout at least aportion of the three-dimensional volume of the body 101. It will beappreciated that the body 101 may include a combination of closedporosity and open porosity.

In accordance with an embodiment, the fixed abrasive article can have abody 101 including a particular content of porosity that can facilitatesuitable material removal operations. For example, the body 101 can havea porosity of at least 0.5 vol % for total volume of the body 101. Inother instances, the content of porosity may be greater, such as atleast 1 vol %, at least 5 vol %, at least 8 vol %, at least 10 vol %, atleast 15 vol %, at least 20 vol %, at least 25 vol %, at least 30 vol %,at least 35 vol %, at least 40 vol %, at least 45 vol %, at least 50 vol%, at least 55 vol %, at least 60 vol %, or even at least 65 vol %.Still, in another non-limiting embodiment, the body 101 can include acontent of porosity that is not greater than 80 vol %, such as notgreater than 75 vol %, not greater than 70 vol %, not greater than 65vol %, not greater than 60 vol %, not greater than 55 vol %, not greaterthan 50 vol %, not greater than 45 vol %, not greater than 40 vol %, notgreater 35 vol %, not greater than 30 vol %, not greater than 25 vol %,not greater than 20 vol %, not greater than 15 vol %, not greater than10 vol %, or even not greater than 5 vol %. It will be appreciated thatthe body 101 can have a content of porosity within a range including anyof the minimum and maximum percentages noted above. For example, thebody can have a content of porosity within a range including at least0.5 vol % and not greater than 80 vol %, such as at least 1 vol % andnot greater than 70 vol %, or even at least 5 vol % and not greater than50 vol %.

In accordance with another embodiment, it will be appreciated that thefixed abrasive article 100 can include a body 101 including certainadditives that may facilitate certain grinding operations. For example,the body 101 can include additives such as fillers, grinding aids, poreinducers, hollow materials, catalysts, coupling agents, curants,antistatic agents, suspending agents, anti-loading agents, lubricants,wetting agents, dyes, fillers, viscosity modifiers, dispersants,defoamers, and a combination thereof.

As further illustrated in FIG. 1 , the body 101 can have a diameter 183,which may be varied according to the desired material removal operation.The diameter can refer to the maximum diameter of the body, particularlyin those cases where the body 101 has a conical or cup-shaped contour.In accordance with an embodiment, the body 101 can have a diameter 183of at least 20 mm, such as at least 50 mm, at least 80 mm, at least 100mm, such as at least 120 mm, at least 150 mm, at least 200 mm, at least400 mm, at least 800 mm, at least 100 cm, at least 200 cm, at least 400cm, or even at least 800 cm. In another embodiment, the diameter 183 ofthe body can be not greater than 4 m, such as not greater than 2 m. Itwill be appreciated the body 101 can have a diameter 183 within a rangeincluding any of the minimum and maximum values noted.

Moreover, the body 101 can have a particular thickness as defined by theaxis 181 extending along the side surface 103 between the upper surface102 and the bottom surface 104 along the axial axis 180. The body 101can have a thickness 181, which may be an average thickness of the body101, which can be not greater than 1 m, such as not greater than 500 cm,not greater than 200 cm, not greater than 100 cm, not greater than 800mm, not greater than 500 mm, not greater than 200 mm, not greater than100 mm, not greater than 80 mm, not greater than 50 mm, not greater than30 mm, or even not greater than 10 mm In one non-limiting embodiment,the body 101 can have a thickness 181, which may be an averagethickness, of at least 1 mm, at least 2 mm, at least 4 mm, at least 8mm, or even at least 10 mm It will be appreciated the body 101 can havea thickness 181 within a range including any of the minimum and maximumvalues noted above.

In accordance with an embodiment, the body 101 may have a particularrelationship between the diameter 183 and thickness 181, defining aratio of diameter:thickness that may be suitable for certain materialremoval operations. For example, the body 101 can have a ratio ofdiameter:thickness of at least 10:1, such as at least 15:1, at least20:1, at least 50:1, or even at least 100:1. It will be appreciated thatthe body may have a ratio of diameter:thickness of not greater than10,000:1 or not greater than 1000:1.

In certain instances, the abrasive particles may have a certain averageparticle size relative to one or more dimensions of the body 101 of thefixed abrasive article, including but not limited to the thickness 181of the body 101. For example, the average particle size (D50), which maybe measured by the longest dimension of the particles, can be less thanthe thickness 181 of the body 101. In particular instances, the abrasiveparticles can have an average particle size that is not greater than 95%of the average thickness of the body, such as not greater than 90%, notgreater than 80%, not greater than 70%, not greater than 60%, notgreater than 50%, not greater than 40%, not greater than 30%, notgreater than 20%, not greater than 10%, not greater than 9%, not greaterthan 8%, not greater than 7%, not greater than 6%, not greater than 5%,not greater than 4%, not greater than 3%, not greater than 2%, or evennot greater than 1% of the average thickness 181 of the body 101. Still,in another non-limiting embodiment, the abrasive particles can have anaverage particle size that is at least 0.001% of the average thicknessof the body 101, such as at least 0.01%, at least 0.1%, at least 1%, atleast 2%, at least 3%, at least 4%, at least 5%, at least 6%, at least7%, at least 8%, at least 9%, at least 10%, at least 11%, at least 12%,at least 15%, at least 20%, or even at least 30% of the averagethickness of the body 101. It will be appreciated that the abrasiveparticles can have a relative average particle size based on the averagethickness of the body within a range including any of the minimum andmaximum percentages noted above, including for example, within a rangeincluding at least 0.001% and not greater than 95%, within a rangeincluding at least 0.01% and not greater than 50%, or even within arange including at least 0.1% and not greater than 20%.

In accordance with an embodiment herein, the fixed abrasive article 100can be a bonded abrasive article including abrasive particles containedwithin the three-dimensional volume of the bond material 107, which canbe distinct from certain other fixed abrasive articles including, forexample, coated abrasive articles, which generally include a singlelayer of abrasive particles contained within a binder, such as a makecoat and/or size coat. Furthermore, coated abrasive articles generallyinclude a backing as a support for the layer of abrasive particles andbinder. By contrast, bonded abrasive articles are generallyself-supporting articles including a three-dimensional volume ofabrasive particles, bond material, and optionally some porosity. Bondedabrasive articles may not necessarily include a substrate, and can beessentially free of a substrate.

The fixed abrasive article 100 may include at least one reinforcingmember 141. In particular instances, the reinforcing material 141 canextend for a majority of the entire width (e.g., the diameter 183) ofthe body 101. However, in other instances, the reinforcing member 141may extend for only a fraction of the entire width (e.g., diameter 183)of the body 101. In certain instances, the reinforcing member 141 may beincluded to add suitable stability to the body for certain materialremoval operations. In accordance with an embodiment, the reinforcingmember 141 can include a material such as a woven material, a nonwovenmaterial, a composite material, a laminated material, a monolithicmaterial, a natural material, a synthetic material, and a combinationthereof. More particularly, in certain instances, the reinforcingmaterial 141 can include a material such as a monocrystalline material,a polycrystalline material, a vitreous material, an amorphous material,a glass (e.g., a glass fiber), a ceramic, a metal, an organic material,an inorganic material, and a combination thereof. In particularinstances, the reinforcing material 141 may include fiberglass, and maybe formed essentially from fiberglass.

In particular instances, the reinforcing material 141 can besubstantially contained within the three-dimensional volume of the body101, more particularly, within the three-dimensional volume of the bondmaterial 107. In certain instances, the reinforcing material 141 mayintersect an exterior surface of the body 101 including, but not limitedto, the upper surface 102, side surface 103, and/or bottom surface 104.For example, the reinforcing material 141 can intersect the uppersurface 102 or bottom surface 104. In at least one embodiment, thereinforcing material 141 may define the upper surface 101 or bottomsurface 104 of the body 101, such that the bond material 107 is disposedbetween one or more reinforcing materials. It will be appreciated thatwhile a single reinforcing member 141 is illustrated in the embodimentof FIG. 1 , a plurality of reinforcing members may be provided withinthe body 101 in a variety of arrangements and orientations suitable forthe intended material removal application.

As further illustrated, the body 101 can include certain axes and planesdefining the three-dimensional volume of the body 101. For example, thebody 101 of the fixed abrasive 100 can include an axial axis 180. Asfurther illustrated along the axial axis 180, the body 101 can include afirst axial plane 131 extending along the axial axis 180 and through aparticular diameter of the body 101 at a particular angular orientation,designated herein as 0°. The body 101 can further include a second axialplane 132 distinct from the first axial plane 131. The second axialplane 132 can extend along the axial axis 180 and through a diameter ofthe body 101 at an angular position, as designated by example herein as30°. The first and second axial planes 131 and 132 of the body 101 maydefine particular axial collections of abrasive particles within thebody 101 including, for example, the axial collection of abrasiveparticles 191 within the axial plane 131 and the axial collection ofabrasive particles 192 within the axial plane 132. Furthermore, theaxial planes of the body 101 may define sectors there between, includingfor example, sector 184 defined as the region between the axial planes131 and 132 within the body 101. The sectors can include a particulargroup of abrasive particles that may facilitate improved materialremoval operations. Reference herein to features of portions of abrasiveparticles within the body, including for example, abrasive particleswithin axial planes will also be relevant to groups of abrasiveparticles contained within one or more sectors of the body.

As further illustrated, the body 101 can include a first radial plane121 extending along a plane that is substantially parallel to the uppersurface 102 and/or bottom surface 104 at a particular axial locationalong the axial axis 180. The body can further include a second radialplane 122, which can extend in a substantially parallel manner to theupper surface 102 and/or bottom surface 104 at a particular axiallocation along the axial axis 180. The first radial plane 121 and secondradial plane 122 can be separated from each other within the body 101,and more particularly, the first radial plane 121 and second radialplane 122 can be axially separated from each other. As furtherillustrated, in certain instances, one or more reinforcing members 141may be disposed between the first and second radial planes 121 and 122.The first and second radial planes 121 and 122 may include one or moreparticular groups of abrasive particles including, for example, thegroup of abrasive particles 106 of the first radial plane 121 and thegroup of abrasive particles 105 of the second radial plane 122, whichmay have certain features relative to each other that may facilitateimproved grinding performance.

The abrasive particles of the embodiments herein can include particulartypes of abrasive particles. For example, the abrasive particles mayinclude shaped abrasive particles and/or elongated abrasive particles,wherein the elongated abrasive particles may have an aspect ratio oflength:width or length:height of at least 1.1:1. Various methods may beutilized to obtain shaped abrasive particles. The particles may beobtained from a commercial source or fabricated. Some suitable processesused to fabricate the shaped abrasive particles can include, but is notlimited to, depositing, printing (e.g., screen-printing), molding,pressing, casting, sectioning, cutting, dicing, punching, pressing,drying, curing, coating, extruding, rolling, and a combination thereof.Similar processes may be utilized to obtain elongated abrasiveparticles. Elongated un-shaped abrasive particles may be formed throughcrushing and sieving techniques.

FIG. 2 includes a perspective view illustration of a shaped abrasiveparticle in accordance with an embodiment. The shaped abrasive particle200 can include a body 201 including a major surface 202, a majorsurface 203, and a side surface 204 extending between the major surfaces202 and 203. As illustrated in FIG. 2 , the body 201 of the shapedabrasive particle 200 is a thin-shaped body, wherein the major surfaces202 and 203 are larger than the side surface 204. Moreover, the body 201can include a longitudinal axis 210 extending from a point or corner ofthe shaped abrasive particle 200 to a base (e.g., an edge of the shapedabrasive particle 200 opposite the point or corner) and through themidpoint 250 on the major surface 202. The longitudinal axis 210 candefine the longest dimension of a major surface while also extendingthrough the midpoint 250 of the major surface. The body 201 can furtherinclude a lateral axis 211 defining a width of the body 201 extendinggenerally perpendicular to the longitudinal axis 210 on the same majorsurface 202. Finally, as illustrated, the body 201 can include avertical axis 212, which in the context of thin shaped bodies can definea height (or thickness) of the body 201. For thin-shaped bodies, thelength of the longitudinal axis 210 is equal to or greater than thevertical axis 212. As illustrated, the thickness 212 can extend alongthe side surface 204 between the major surfaces 202 and 203 andperpendicular to the plane defined by the longitudinal axis 210 andlateral axis 211. It will be appreciated that reference herein tolength, width, and height of the abrasive particles may be referenced toaverage values taken from a suitable sampling size of abrasive particlesof a batch.

The shaped abrasive particles can include any of the features of theabrasive particles of the embodiments herein. For example, the shapedabrasive particles can include a crystalline material, and moreparticularly, a polycrystalline material. Notably, the polycrystallinematerial can include abrasive grains. In one embodiment, the body of theabrasive particle, including for example, the body of a shaped abrasiveparticle can be essentially free of an organic material, including forexample, a binder. In at least one embodiment, the abrasive particlescan consist essentially of a polycrystalline material.

Some suitable materials for use as abrasive particles can includenitrides, oxides, carbides, borides, oxynitrides, oxyborides, diamond,carbon-containing materials, and a combination thereof. In particularinstances, the abrasive particles can include an oxide compound orcomplex, such as aluminum oxide, zirconium oxide, titanium oxide,yttrium oxide, chromium oxide, strontium oxide, silicon oxide, magnesiumoxide, rare-earth oxides, and a combination thereof. In one particularembodiment, the abrasive particles can include at least 95 wt % aluminafor the total weight of the body. In at least one embodiment, theabrasive particles can consist essentially of alumina. Still, in certaininstances, the abrasive particles can include not greater than 99.5 wt %alumina for the total weight of the body. Moreover, in particularinstances, the shaped abrasive particles can be formed from a seededsol-gel. In at least one embodiment, the abrasive particles of theembodiments herein may be essentially free of iron, rare-earth oxides,and a combination thereof.

The abrasive grains (i.e., crystallites) contained within the body ofthe abrasive particles may have an average grain size that is generallynot greater than about 100 microns. In other embodiments, the averagegrain size can be less, such as not greater than about 80 microns, notgreater than about 50 microns, not greater than about 30 microns, notgreater than about 20 microns, not greater than about 10 microns, notgreater than about 1 micron, not greater than about 0.9 microns, notgreater than about 0.8 microns, not greater than about 0.7 microns, oreven not greater than about 0.6 microns. Still, the average grain sizeof the abrasive grains contained within the body of the abrasiveparticles can be at least about 0.01 microns, such as at least about0.05 microns, at least about 0.06 microns, at least about 0.07 microns,at least about 0.08 microns, at least about 0.09 microns, at least about0.1 microns, at least about 0.12 microns, at least about 0.15 microns,at least about 0.17 microns, at least about 0.2 microns, or even atleast about 0.5 microns. It will be appreciated that the abrasive grainscan have an average grain size within a range between any of the minimumand maximum values noted above.

In accordance with certain embodiments, certain abrasive particles canbe composite articles including at least two different types of grainswithin the body of the abrasive particle. It will be appreciated thatdifferent types of grains are grains having different compositions,different crystallite sizes, and/or different grit sizes with regard toeach other. For example, the body of the abrasive particle can be formedsuch that is includes at least two different types of grains, whereinthe two different types of grains can be nitrides, oxides, carbides,borides, oxynitrides, oxyborides, diamond, and a combination thereof.

In accordance with an embodiment, the abrasive particles can have anaverage particle size, as measured by the largest dimension (i.e.,length) of at least about 100 microns. In fact, the abrasive particlescan have an average particle size of at least about 150 microns, such asat least about 200 microns, at least about 300 microns, at least about400 microns, at least about 500 microns, at least about 600 microns, atleast about 700 microns, at least about 800 microns, or even at leastabout 900 microns. Still, the abrasive particles of the embodimentsherein can have an average particle size that is not greater than about5 mm, such as not greater than about 3 mm, not greater than about 2 mm,or even not greater than about 1.5 mm. It will be appreciated that theabrasive particles can have an average particle size within a rangebetween any of the minimum and maximum values noted above.

FIG. 2 includes an illustration of a shaped abrasive particle having atwo-dimensional shape as defined by the planes of the major surfaces 202or 203, each of which has a generally triangular two-dimensional shape.It will be appreciated that the shaped abrasive particles of theembodiments herein are not so limited and can include othertwo-dimensional shapes. For example, the shaped abrasive particles ofthe embodiment herein can include particles having a body with atwo-dimensional shape as defined by a major surface of the body from thegroup of shapes including polygons, irregular polygons, irregularpolygons including arcuate or curved sides or portions of sides,ellipsoids, numerals, Greek alphabet characters, Latin alphabetcharacters, Russian alphabet characters, Kanji characters, complexshapes having a combination of polygons shapes, star shapes, and acombination thereof.

FIG. 3A includes a perspective view illustration of a shaped abrasiveparticle according to an embodiment. Notably, the shaped abrasiveparticle 300 can include a body 301 including a surface 302 and asurface 303, which may be referred to as end surfaces 302 and 303. Thebody can further include surfaces 304, 305, 306, 307 extending betweenand coupled to the end surfaces 302 and 303. The shaped abrasiveparticle of FIG. 3A is an elongated shaped abrasive particle having alongitudinal axis 310 that extends along the surface 305 and through themidpoint 340 between the end surfaces 302 and 303. It will beappreciated that the surface 305 is selected for illustrating thelongitudinal axis 310, because the body 301 has a generally squarecross-sectional contour as defined by the end surfaces 302 and 303. Assuch, the surfaces 304, 305, 306, and 307 have approximately the samesize relative to each other. However, in the context of other elongatedabrasive particles wherein the surfaces 302 and 303 define a differentshape, for example a rectangular shape, wherein one of the surfaces 304,305, 306, and 307 may be larger relative to the others, the largest ofthose surfaces defines the major surface and, therefore, thelongitudinal axis would extend along the largest of those surfaces. Asfurther illustrated, the body 301 can include a lateral axis 311extending perpendicular to the longitudinal axis 310 within the sameplane defined by the surface 305. As further illustrated, the body 301can further include a vertical axis 312 defining a height of theabrasive particle, wherein the vertical axis 312 extends in a directionperpendicular to the plane defined by the longitudinal axis 310 andlateral axis 311 of the surface 305.

It will be appreciated that, like the thin shaped abrasive particle ofFIG. 2 , the elongated shaped abrasive particle of FIG. 3A can havevarious two-dimensional shapes such as those defined with respect to theshaped abrasive particle of FIG. 2 . The two-dimensional shape of thebody 301 can be defined by the shape of the perimeter of the endsurfaces 302 and 303. The elongated shaped abrasive particle 300 canhave any of the attributes of the shaped abrasive particles of theembodiments herein.

FIG. 3B includes an illustration of an elongated particle, which is nota shaped abrasive particle. Shaped abrasive particles may be formedthrough particular processes, including molding, printing, casting,extrusion, and the like. Shaped abrasive particles are formed such thateach particle has substantially the same arrangement of surfaces andedges relative to each other. For example, a group of shaped abrasiveparticles generally have the same arrangement and orientation and ortwo-dimensional shape of the surfaces and edges relative to each other.As such, the shaped abrasive particles have a high shape fidelity andconsistency in the arrangement and orientation of the surfaces and edgesrelative to each other. By contrast, non-shaped abrasive particles, canbe formed through different processes and have different shapeattributes. For example, crushed grains are typically formed by acomminution process wherein a mass of material is formed and thencrushed and sieved to obtain abrasive particles of a certain size.However, a non-shaped abrasive particle will have a generally randomarrangement of the surfaces and edges, and generally will lack anyrecognizable two-dimensional or three dimensional shape in thearrangement of the surfaces and edges. Moreover, the non-shaped abrasiveparticles do not necessarily have a consistent shape with respect toeach other and therefore have a significantly lower shape fidelitycompared to shaped abrasive particles. The non-shaped abrasive particlesgenerally are defined by a random arrangement of surfaces and edges withrespect to each other.

As further illustrated in FIG. 3B, the elongated abrasive article can bea non-shaped abrasive particle having a body 351 and a longitudinal axis352 defining the longest dimension of the particle, a lateral axis 353extending perpendicular to the longitudinal axis 352 and defining awidth of the particle. Furthermore, the elongated abrasive particle mayhave a height (or thickness) as defined by the vertical axis 354 whichcan extend generally perpendicular to a plane defined by the combinationof the longitudinal axis 352 and lateral axis 353. As furtherillustrated, the body 351 of the elongated, non-shaped abrasive particlecan have a generally random arrangement of edges 355 extending along theexterior surface of the body 351.

As will be appreciated, the elongated abrasive particle can have alength defined by longitudinal axis 352, a width defined by the lateralaxis 353, and a vertical axis 354 defining a height. As will beappreciated, the body 351 can have a primary aspect ratio oflength:width such that the length is greater than the width.Furthermore, the length of the body 351 can be greater than or equal tothe height. Finally, the width of the body 351 can be greater than orequal to the height 354. In accordance with an embodiment, the primaryaspect ratio of length:width can be at least 1.1:1, at least 1.2:1, atleast 1.5:1, at least 1.8:1, at least 2:1, at least 3:1, at least 4:1,at least 5:1, at least 6:1, or even at least 10:1. In anothernon-limiting embodiment, the body 351 of the elongated abrasive particlecan have a primary aspect ratio of length:width of not greater than100:1, not greater than 50:1, not greater than 10:1, not greater than6:1, not greater than 5:1, not greater than 4:1, not greater than 3:1,or even not greater than 2:1. It will be appreciated that the primaryaspect ratio of the body 351 can be with a range including any of theminimum and maximum ratios noted above.

Furthermore, the body 351 of the elongated abrasive particle 350 caninclude a secondary aspect ratio of width:height that can be at least1.1:1, such as at least 1.2:1, at least 1.5:1, at least 1.8:1, at least2:1, at least 3:1, at least 4:1, at least 5:1, at least 8:1, or even atleast 10:1. Still, in another non-limiting embodiment, the secondaryaspect ratio width:height of the body 351 can be not greater than 100:1,such as not greater than 50:1, not greater than 10:1, not greater than8:1, not greater than 6:1, not greater than 5:1, not greater than 4:1,not greater than 3:1, or even not greater than 2:1. It will beappreciated the secondary aspect ratio of width:height can be with arange including any of the minimum and maximum ratios of above.

In another embodiment, the body 351 of the elongated abrasive particle350 can have a tertiary aspect ratio of length:height that can be atleast 1.1:1, such as at least 1.2:1, at least 1.5:1, at least 1.8:1, atleast 2:1, at least 3:1, at least 4:1, at least 5:1, at least 8:1, oreven at least 10:1. Still, in another non-limiting embodiment, thetertiary aspect ratio length:height of the body 351 can be not greaterthan 100:1, such as not greater than 50:1, not greater than 10:1, notgreater than 8:1, not greater than 6:1, not greater than 5:1, notgreater than 4:1, or even not greater than 3:1. It will be appreciatedthat the tertiary aspect ratio of the body 351 can be within a rangeincluding any of the minimum and maximum ratios and above.

The elongated abrasive particle 350 can have certain attributes of theother abrasive particles described in the embodiments herein including,but not limited to, composition, microstructural features (e.g., averagegrain size), hardness, porosity, and the like.

FIG. 4A includes a top view illustration of a shaped abrasive particleaccording to an embodiment. In particular, the shaped abrasive particle400 can include a body 401 having the features of other shaped abrasiveparticles of embodiments herein, including an upper major surface 403and a bottom major surface (not shown) opposite the upper major surface403. The upper major surface 403 and the bottom major surface can beseparated from each other by at least one side surface 405, which mayinclude one or more discrete side surface portions, including forexample, a first portion 406 of the side surface 405, a second portion407 of the side surface 405, and a third portion 408 of the side surface405. In particular, the first portion 406 of the side surface 405 canextend between a first corner 409 and a second corner 410. The secondportion 407 of the side surface 405 can extend between the second corner410 and a third corner 411. Notably, the second corner 410 can be anexternal corner joining two portions of the side surface 405. The secondcorner 410 and a third corner 411, which is also an external corner, areadjacent to each other and have no other external corners disposedbetween them. Also, the third portion 408 of the side surface 405 canextend between the third corner 411 and the first corner 409, both ofwhich are external corners that are adjacent to each other and have noother external corners disposed between them.

As illustrated, the body 401 can include a first portion 406 including afirst curved section 442 disposed between a first linear section 441 anda second linear section 443 and between the external corners 409 and410. The second portion 407 is separated from the first portion 406 ofthe side surface 405 by the external corner 410. The second portion 407of the side surface 405 can include a second curved section 452 joininga third linear section 451 and a fourth linear section 453. Furthermore,the body 401 can include a third portion 408 separated from the firstportion 406 of the side surface 405 by the external corner 409 andseparated from the second portion 407 by the external corner 411. Thethird portion 408 of the side surface 405 can include a third curvedsection 462 joining a fifth linear section 461 and a sixth linearsection 463.

FIG. 4B includes a top view of a shaped abrasive particle 430 accordingto an embodiment. The tip sharpness of a shaped abrasive particle, whichmay be an average tip sharpness, may be measured by determining theradius of a best fit circle on an external corner 431 of the body 432.For example, a top view of the upper major surface 433 of the body 432is provided. At an external corner 431, a best fit circle is overlaid onthe image of the body 432 of the shaped abrasive particle 430, and theradius of the best fit circle relative to the curvature of the externalcorner 431 defines the value of tip sharpness for the external corner431. The measurement may be recreated for each external corner of thebody 432 to determine the average individual tip sharpness for a singleshaped abrasive particle 430. Moreover, the measurement may be recreatedon a suitable sample size of shaped abrasive particles of a batch ofshaped abrasive particles to derive the average batch tip sharpness. Anysuitable computer program, such as ImageJ may be used in conjunctionwith an image (e.g., SEM image or light microscope image) of suitablemagnification to accurately measure the best fit circle and the tipsharpness.

The shaped abrasive particles of the embodiments herein may have aparticular tip sharpness that may facilitate suitable performance in thefixed abrasive articles of the embodiments herein. For example, the bodyof a shaped abrasive particle can have a tip sharpness of not greaterthan 80 microns, such as not greater than 70 microns, not greater than60 microns, not greater than 50 microns, not greater than 40 microns,not greater than 30 microns, not greater than 20 microns, or even notgreater than 10 microns. In yet another non-limiting embodiment, the tipsharpness can be at least 2 microns, such as at least 4 microns, atleast 10 microns, at least 20 microns, at least 30 microns, at least 40microns, at least 50 microns, at least 60 microns, or even at least 70microns. It will be appreciated that the body can have a tip sharpnesswithin a range between any of the minimum and maximum values notedabove.

Another grain feature of shaped abrasive particles is the Shape Index.The Shape Index of a body of a shaped abrasive particle can be describedas a value of an outer radius of a best-fit outer circle superimposed onthe body, as viewed in two dimensions of a plane of length and width ofthe body (e.g., the upper major surface or the bottom major surface),compared to an inner radius of the largest best-fit inner circle thatfits entirely within the body, as viewed in the same plane of length andwidth. For example, turning to FIG. 4C, a shaped abrasive particle isprovided with two circles superimposed on the illustration todemonstrate the calculation of Shape Index. A first circle issuperimposed on the body 470 of the shaped abrasive particle, which is abest-fit outer circle representing the smallest circle that can be usedto fit the entire perimeter of the body 470 within its boundaries. Theouter circle has a radius (Ro). For shapes such as that illustrated inFIG. 4C, the outer circle may intersect the perimeter of the body ateach of the three external corners. However, it will be appreciated thatfor certain irregular or complex shapes, the body may not fit uniformlywithin the circle such that each of the corners intersect the circle atequal intervals, but a best-fit, outer circle still may be formed. Anysuitable computer program, such as ImageJ, may be used in conjunctionwith an image of suitable magnification (e.g., SEM image or lightmicroscope image) to create the outer circle and measure the radius(Ro).

A second, inner circle can be superimposed on the body 470, asillustrated in FIG. 4C, which is a best fit circle representing thelargest circle that can be placed entirely within the perimeter of thebody 470 as viewed in the plane of the length and width of the body 470.The inner circle can have a radius (Ri). It will be appreciated that forcertain irregular or complex shapes, the inner circle may not fituniformly within the body such that the perimeter of the circle contactsportions of the body at equal intervals, such as shown for the shape ofFIG. 4C. However, a best-fit, inner circle still may be formed. Anysuitable computer program, such as ImageJ, may be used in conjunctionwith an image of suitable magnification (e.g., SEM image or lightmicroscope image) to create the inner circle and measure the radius(Ri).

The Shape Index can be calculated by dividing the outer radius by theinner radius (i.e., Shape Index=Ri/Ro). For example, the body 470 of theshaped abrasive particle has a Shape Index of approximately 0.35.Moreover, an equilateral triangle generally has a Shape Index ofapproximately 0.5, while other polygons, such as a hexagon or pentagonhave Shape Index values greater than 0.5. In accordance with anembodiment, the shaped abrasive particles herein can have a Shape Indexof at least 0.02, such as at least 0.05, at least 0.10, at least 0.15,at least 0.20, at least 0.25, at least 0.30, at least 0.35, at least0.40, at least 0.45, at least about 0.5, at least about 0.55, at least0.60, at least 0.65, at least 0.70, at least 0.75, at least 0.80, atleast 0.85, at least 0.90, or at least 0.95. Still, in anothernon-limiting embodiment, the shaped abrasive particle can have a ShapeIndex of not greater than 1, such as not greater than 0.98, not greaterthan 0.95, not greater than 0.90, not greater than 0.85, not greaterthan 0.80, not greater than 0.75, not greater than 0.70, not greaterthan 0.65, not greater than 0.60, not greater than 0.55, not greaterthan 0.50, not greater than 0.45, not greater than 0.40, not greaterthan 0.35, not greater than 0.30, not greater than 0.25, not greaterthan 0.20, not greater than 0.15, not greater than 0.10, not greaterthan 0.05, or not greater than 0.02. It will be appreciated that theshaped abrasive particles can have a Shape Index within a range betweenany of the minimum and maximum values noted above.

FIG. 4D includes a top view of a shaped abrasive particle according toanother embodiment. The shaped abrasive particle 480 can have a body 481having the features of other shaped abrasive particles of embodimentsherein, including an upper major surface 483 and a bottom major surface(not shown) opposite the upper major surface 483. The upper majorsurface 483 and the bottom major surface can be separated from eachother by at least one side surface 484, which may include one or morediscrete side surface sections. According to one embodiment, the body481 can be defined as an irregular hexagon, wherein the body has ahexagonal (i.e., six-sided) two dimensional shape as viewed in the planeof a length and a width of the body 481, and wherein at least two of thesides, such as sides 485 and 486, have a different length with respectto each other. Notably, the length of the sides is understood herein torefer to the width of the body 481 and the length of the body is thegreatest dimension extending through the midpoint of the body 481.Moreover, as illustrated, none of the sides are parallel to each other.And furthermore, while not illustrated, any of the sides may have acurvature to them, including a concave curvature wherein the sides maycurve inwards toward the interior of the body 481.

In accordance with an embodiment, the abrasive particles, which caninclude shaped abrasive particles and/or elongated abrasive particles,can be placed within the body 101 of the fixed abrasive article 100depicted in FIG. 1 such that the abrasive particles have a predeterminedposition and/or predetermined three-axis orientation within the body101. FIG. 5A includes an illustration of a first group of abrasiveparticles 545 within an axial plane, such as the axial plane 131 of thebody 101 (as depicted in FIG. 1 ). As illustrated, the first group 545can include a plurality of abrasive particles, including abrasiveparticles 502, 503, 504, 505, and 506 (502-506). The first group 545 mayfurther include abrasive particles 522, 523, 524, 525, and 526(522-526). Unlike conventional fixed abrasive articles, includingconventional bonded abrasive articles, where the abrasive particles arerandomly positioned and randomly oriented within the volume of the body,the fixed abrasive articles of the embodiments herein include abrasiveparticles in a predetermined position within the three-dimensionalvolume of the body 101. Furthermore, the abrasive particles of theembodiments herein can be placed within the three-dimensional volume ofthe body with a predetermined three-axis orientation. The provision ofthe abrasive particles in a predetermined position and/or predeterminedthree-axis orientation may facilitate improved material removalperformance of the fixed abrasive article compared to conventional fixedabrasive articles having abrasive particles randomly positioned andoriented within the body.

The first group of abrasive particles 545 within the axial plane caneach have a predetermined three-axis orientation including apredetermined rotational orientation relative to a major surface, suchas the upper surface 102 of the body 101. For example, the shapedabrasive particle 502 can have a longitudinal axis 511. The longitudinalaxis 511 extends from a point or corner of the shaped abrasive particle502 through the midpoint of a major surface of the shaped abrasiveparticle 502. In an embodiment and as shown in FIG. 5A, the longitudinalaxis 511 can be substantially aligned with an axial axis 512 of the body101. The axial axis 512 is an axis of the body 101 that is within theaxial plane (e.g., axial plane 131) and that extends through a midpointof the major surface of the particle defining the longitudinal axis 511of the particle. Furthermore, the axial axis is substantiallyperpendicular to the major surface (e.g., upper surface 102) of the body101 to which the abrasive particle is most closely positioned. Apredetermined tilt angle is the angle between the longitudinal axis 511of the shaped abrasive particle (or elongated particle) and the axialaxis 512 in a plane defined by a length and a width of the shapedabrasive particle 502. More specifically, the predetermined tilt angleis measured at the point along the longitudinal axis 511 closest to theupper surface 102. Therefore, a predetermined tilt angle of the shapedabrasive particle 502 relative to the upper surface 102 in FIG. 5A issubstantially 0°. In accordance with an embodiment, at least a portionof the abrasive particles within the fixed abrasive article 100 can havea predetermined tilt angle that is less than 90°. For example, theaverage predetermined tilt angle for a portion of the abrasive particlescan be not greater than 90°, such as not greater than 80°, not greaterthan 70°, not greater than 60°, not greater than 50°, not greater than40°, not greater than 30°, not greater than 20°, not greater than 10°,or not greater than 5°. Still, in another non-limiting embodiment, theaverage predetermined tilt angle for a portion of the abrasive particleswithin the body 101 can be at least 0.1°, such as at least 1°, at least3°, at least 5°, at least 10°, at least 20°, at least 30°, at least 40°,or even at least 50°. It will be appreciated that the averagepredetermined tilt angle may be controlled to facilitate improvedgrinding performance of the fixed abrasive article. Furthermore, theaverage predetermined tilt angle for a portion of the abrasive particlesin the body 101 can be within a range including any of the minimum andmaximum angles noted above.

For any of the embodiments herein, reference to a portion of theabrasive particles having a predetermined tilt angle can include atleast a content of abrasive particles, particularly shaped abrasiveparticles and/or elongated abrasive particles, which is distinct fromconventional articles having a random orientation of the abrasiveparticles. For example, a portion of abrasive particles in the body caninclude at least 10%, such as at least 20%, at least 30%, at least 40%,at least 50%, at least 60%, at least 70%, at least 80%, or even at least90% of the total abrasive particles within the body 101. In accordancewith a particular embodiment, essentially all of the abrasive particles,including only the shaped abrasive particles and/or elongated abrasiveparticles, can have a predetermined tilt angle within a range includingany of the minimum and maximum values noted above. Moreover, as will beunderstood in light of the entire disclosure and embodiments herein, aportion of abrasive particles within the body 101 can include a group ofabrasive particles (e.g., a first group of abrasive particles in aradial plane or in a sector), a radial set of abrasive particles, anaxial collection of abrasive particles, an axial set of abrasiveparticles, and a combination thereof.

Furthermore, at least a portion of the abrasive particles, including theshaped abrasive particles and/or elongated abrasive particles within thebody 101, may have a standard deviation of predetermined tilt angle. Alow standard deviation indicates a high degree of control of thepredetermined tilt angle for that portion of the abrasive particleshaving the predetermined tilt angle within the body 101. For example, inaccordance with an embodiment, the portion of abrasive particles withinthe body 101 can have a standard deviation of the predetermined tiltangle of not greater than 20 degrees, not greater than 18 degrees, notgreater than 16 degrees, not greater than 14 degrees, not greater than12 degrees, not greater than 10 degrees, not greater than 9 degrees, notgreater than 8 degrees, not greater than 7 degrees, or even not greaterthan 6 degrees. Still, in at least one non-limiting embodiment, theportion of the abrasive particles in the body 101 can have a standarddeviation of the predetermined tilt angle of at least 0.01 degrees, suchas at least 0.1 degrees, or even at least 1 degree. It will beappreciated that the standard deviation of the predetermined tilt anglecan be within a range including any of the minimum maximum values notedabove. Reference herein to a portion of the abrasive particles withinthe body 101 having a standard deviation predetermined tilt angle can bereference to a portion of abrasive particles within the body asdescribed herein.

Referring briefly to FIG. 5B, an illustration of a shaped abrasiveparticle contained in a body of a fixed abrasive in a predeterminedthree-axis orientation is provided. Reference to a predeterminedthree-axis orientation includes the control of the three axes definingthe shaped abrasive particle 502 (including the longitudinal axis 511extending through a midpoint 584 of a first major surface 581, thelateral axis 586, and the vertical axis 587) within the body 101 and,more particularly, relative to a major surface (e.g., the upper surface102 and/or bottom surface 104) of the body 101. In particular, theshaped abrasive particle 502 can be standing up within the body 101relative to a major surface of the body. The shaped abrasive particle502 can have a first major surface 581, a second major surface 582, anda side surface 583 extending between the first and second major surfaces581 and 582. The longitudinal axis 511, extending between a tip orcorner of the shaped abrasive particle 502 and a base or edge oppositethat tip/corner and also extending through the midpoint 584, can extendsubstantially perpendicular to a major surface of the body 101, such asthe upper surface 102 and/or bottom surface 104. Moreover, for theshaped abrasive particle 502, the longitudinal axis 511 can extendsubstantially parallel to the side surface 103 of the body 101. This maybe particularly advantageous for fixed abrasive articles where the majorsurface, such as the upper surface 102, is configured to conduct theprimary material removal operations. As such, it may be particularlysuitable for the shaped abrasive particles and/or elongated abrasiveparticles to have a three-axis orientation, including a predeterminedrotational orientation relative to a major surface of the body 101.

As further illustrated in FIG. 5B, the lateral axis 586 defining a widthof the shaped abrasive particle 502 also can extend substantiallyparallel to a major surface of the body 101, such as the upper surface102 of the body 101. Moreover, in some embodiments, the lateral axis 586can extend substantially parallel to a tangent 589 of the upper surface102 of the body 101 at the point where the axial axis 512 intersects theupper surface 102. As further illustrated in FIG. 5B, the vertical axis587 defining the height of the shaped abrasive particle 502 can extendsubstantially parallel to a major surface of the body 101, such as theupper surface 102 of the body 101. Moreover, in some embodiments, thevertical axis 587 can extend substantially parallel to a tangent 588 ofthe upper surface 102 of the body 101 at the point where the axial axis512 intersects the upper surface 102.

The shaped abrasive particle 502 illustrates an abrasive particle in astanding orientation relative to a major surface of the body of thefixed abrasive. The embodiments herein further include abrasiveparticles, including shaped abrasive particles or elongated abrasiveparticles, which can be tilted relative to a major surface of the body.For example, FIG. 5B includes an illustration of a shaped abrasiveparticle 522 in a tilted orientation relative to a major surface, suchas the upper surface 102 of the body 101. As illustrated, the shapedabrasive particle 522 can have a first major surface 561, a second majorsurface 562, and a side surface 563 extending between the first andsecond major surfaces 561 and 562. The longitudinal axis 531, extendingbetween a tip or corner of the shaped abrasive particle 522 and a baseor edge opposite that tip/corner and also extending through the midpoint566, can extend at an angle relative to an axial axis 512 that isperpendicular to a major surface (e.g., the upper surface 102 and/orbottom surface 104 of the body 101). The angle 532 between thelongitudinal axis 531 and the axial axis 512 defines the predeterminedtilt angle 532 of the shaped abrasive particle 522. It will beappreciated that the shaped abrasive particle 522 can be tilted along anaxis defined by the lateral axis 564 defining the width, the verticalaxis 565 defining the height, and a combination thereof. For example,the shaped abrasive particle may be tilted at a 45 degree angle relativeto the lateral axis 564 and vertical axis 565. In an embodiment, apredetermined vertical rotational orientation angle is the angle betweena vertical axis of the shaped abrasive particle or elongated particle(e.g., vertical axis 565) and an axial axis of the body 101 (e.g., theaxial axis 512) in a plane defined by a length and a thickness of theshaped abrasive particle 522.

In another embodiment, at least a portion of the abrasive particles inthe body may have a predetermined rotational orientation relative to anintended grinding direction 546 (in FIG. 5A) of the abrasive article.For example, the predetermined vertical rotational orientation angle canalso define a rake angle relative to the intended grinding direction 546of the abrasive article 100. In the instance of the shaped abrasiveparticle 502, the rake angle has a zero value because the shapedabrasive particle 502 has a predetermined vertical rotationalorientation angle that orients the cutting tip 547 substantiallyperpendicular to the intended grinding direction 546. In the instance ofthe shaped abrasive particle 522 (FIG. 5B), the rake angle can have apositive value if the shaped abrasive particle 522 has a predeterminedvertical rotational orientation angle that inclines the cutting tip 548in the same direction as the intended grinding direction 546. In anotherembodiment, a shaped abrasive particle can include a rake angle with anegative value, where a shaped abrasive particle has a predeterminedvertical rotational orientation angle that inclines a cutting tip in adirection opposite to the intended grinding direction 546. As such, itwill be appreciated that the abrasive particles and the orientation oftheir cutting tips or cutting surfaces relative to the upper surface maybe controlled such that a suitable rake angle is created relative to anintended grinding direction 546 of the abrasive article 100, which mayfacilitate improved material removal performance.

Referring again to FIG. 5A, the first group of abrasive particles 545can include a first portion of abrasive particles having substantiallythe same predetermined three-axis orientation relative to a majorsurface, such as the upper surface 102, of the body 101. For example,the abrasive particles 502-506, which are shaped abrasive particleswhose major surfaces have a triangular two-dimensional shape, can havesubstantially the same three-axis orientation relative to the uppersurface 102. More particularly, the abrasive particles 502-506 can havesubstantially the same predetermined tilt angle relative to the uppersurface 102. As illustrated in the embodiment of FIG. 5A, the abrasiveparticle 502 has a longitudinal axis 511 that is substantially alignedwith the axial axis 512, thereby defining a predetermined tilt angle ofapproximately 0° at the point where the longitudinal axis 511 is closestto the major surface (e.g., the upper surface 102). Likewise, theabrasive particle 503 includes a longitudinal axis 513 that issubstantially aligned with the axial axis 514. Therefore, the abrasiveparticle 503 also has a predetermined tilt angle of approximately 0° atthe point where the longitudinal axis 513 is closest to the uppersurface 102. Furthermore, abrasive particle 504 has a longitudinal axis515 that is substantially aligned with axial axis 516. Therefore, theabrasive particle 504 has a predetermined tilt angle of approximately 0°at the point where the longitudinal axis 515 is closest to the uppersurface 10. The abrasive particle 505 has a longitudinal axis 517 thatis substantially aligned with the axial axis 518, also defining apredetermined tilt angle of approximately 0°. Moreover, the abrasiveparticle 506 has a longitudinal axis 519 substantially aligned with theaxial axis 520, thereby defining a predetermined tilt angle ofapproximately 0°. Accordingly, the abrasive particles 502-506 can havesubstantially the same predetermined rotational orientation relative tothe upper surface 102 as defined by the respective predetermined tiltangles associated with each of the abrasive particles 502-506. Moreover,it will be appreciated that each of the abrasive particles 502-506 havesubstantially the same orientation of their lateral axes and verticalaxes relative to the corresponding axial axes 512, 514, 516, 518, and520 and the upper surface 102. Moreover, while the shaped abrasiveparticles of FIG. 5A are illustrated as having generally triangulartwo-dimensional shapes, other types of shaped abrasive particles and/orelongated abrasive particles may be utilized. As further illustrated inFIG. 5A, at least a portion of the abrasive particles within the body101 can be arranged in a controlled distribution relative to each other.A controlled distribution can be defined by a combination ofpredetermined positions within the body that are purposefully selectedto be occupied by the abrasive particles. A controlled distribution caninclude a pattern, such that the predetermined positions can define atwo-dimensional array. An array can include have short range orderdefined by a unit of abrasive particles. An array may also be a patternhaving long range order, including regular and repetitive units linkedtogether, such that the arrangement may be symmetrical and/orpredictable. An array may have an order that can be predicted by amathematical formula. It will be appreciated that two-dimensional arrayscan be formed in the shape of polygons, ellipsis, ornamental indicia,product indicia, or other designs. A controlled or predetermineddistribution can also include a non-shadowing arrangement. Anon-shadowing arrangement may include a controlled, non-uniformdistribution, a controlled uniform distribution, and a combinationthereof. In particular instances, a non-shadowing arrangement mayinclude a radial pattern, a spiral pattern, a phyllotactic pattern, anasymmetric pattern, a self-avoiding random distribution, and acombination thereof. In other instances, a non-shadowing arrangement caninclude an intentional staggering of two or more particles relative toone another (e.g., an intentional staggering of two or morepredetermined positions and/or predetermined rotational orientations),as discussed more fully with respect to FIG. 8 .

According to one embodiment, the first group 545 of abrasive particlesis arranged in a controlled distribution relative to each other withinan axial plane (e.g., the axial plane 131 of the body 101). As will beappreciated, each of the abrasive particles within the first group 545can have substantially the same angular position within the body 101 andtherefore are located within the axial plane 131. The abrasive particlescontained within the first group 545 may have different radial positionswith respect to each other. For example, the abrasive particles 522-526can have a different radial position relative to one another and adifferent axial position relative to the abrasive particles 502-506. Itwill be appreciated that reference to the radial position can bereferenced to the position of the abrasive particles along a radialaxis, including for example radial axis 567, which can extend radiallyoutward from a center of the body.

Referring to FIG. 5C, a view of an axial plane 596 of abrasive particleswithin a body of a fixed abrasive article is illustrated. As shown, theabrasive particles within the axial plane of the body can be arranged invarious controlled distributions with respect to each other. Forexample, the abrasive particles of the first group 591 can be arrangedin a controlled distribution that has a generally rectangular pattern,such that the smallest unit 595 of abrasive particles defines arectangle or square. As will be appreciated and as illustrated, othertypes of controlled distributions may be utilized. In certain instances,different groups of abrasive particles within the axial plane 596 candefine different controlled distributions. For example, as illustrated,the abrasive particles of the group 592 may be arranged in a differentcontrolled distribution relative to those abrasive particles of thefirst group 591. Likewise, the abrasive particles of the group 593 canbe arranged in yet another controlled distribution relative to groups591 and 592. Moreover, as illustrated, abrasive particles within thesame axial plane 596 but on opposite sides of the opening 185 of thebody 101 can define different controlled distributions. Finally, theabrasive particles of the group 594 may have a different controlleddistribution relative to the abrasive particles of the groups 593, 592,and 591. The controlled distributions provided in FIG. 5C are merelyillustrative and are non-limiting. Various controlled distributions maybe utilized to improve the grinding performance of the fixed abrasivearticle.

The predetermined position of the abrasive particles relative to eachother can define the controlled distribution. For example, referringagain to FIG. 5A, the abrasive particles 502-506 can be spaced apartfrom each other in a predetermined manner, which may facilitate improvedmaterial removal operations. For example, as illustrated, the abrasiveparticle 502 can be spaced apart from the abrasive particle 503 by aspacing distance 551 defined as the smallest distance between theabrasive particles 502 and 503. Moreover, the abrasive particle 503 canbe spaced apart from the abrasive particle 504 by a spacing distance552, the abrasive particle 504 can be spaced apart from the abrasiveparticle 505 by a spacing distance 553, and the abrasive particle 505can be spaced apart from the abrasive particle 506 by a spacing distance554. According to an embodiment, at least a portion of the abrasiveparticles within the body can have substantially the same spacingdistance, including for example, the spacing distances 551-554 betweenthe abrasive particles 502-504. The portion can include any portion ofabrasive particles as described in embodiments herein.

Furthermore, a suitable spacing distance between particles may be basedon the average particle size (PSa) of the portion of abrasive particles,wherein the average particle size of shaped abrasive particles is basedon the length of the particles and the spacing distance can be anaverage spacing distance between the abrasive particles. For example,the spacing distance for a portion of the abrasive particles within thebody can be not greater than 10 (PSa), such as not greater than 9 (PSa),not greater than 8 (PSa), not greater than 7 (PSa), such as not greaterthan 6 (PSa), not greater than 5 (PSa), not greater than 4 (PSa), suchas not greater than 3 (PSa), not greater than 2 (PSa), not greater than1 (PSa), such as not greater than 0.8 (PSa), not greater than 0.5 (PSa),not greater than 0.4 (PSa), or even not greater than 0.2 (PSa). In atleast one embodiment, the spacing distance for a portion of abrasiveparticles can be 0, such that the abrasive particles are in contact witheach other, which may be particularly desirable for certain materialremoval operations. Still, in another non-limiting embodiment, thespacing distance can be at least 0.1 (PSa), at least about 0.2 (PSa), atleast 0.5 (PSa), at least 0.8 (PSa), at least 1 (PSa), at least 2 (PSa),or even at least 3 (PSa). It will be appreciated that the spacingdistance can be within a range including any of the minimum and maximumvalues noted above.

In still another embodiment, the portion of abrasive particles can havea particularly low standard deviation of spacing distance, which candemonstrate the level of control in the predetermined positioning of theabrasive particles within the body. For example, the standard deviationof the spacing distance can be not greater than 2 (PSa), such as notgreater than 1.8 (PSa), not greater than 1.5 (PSa), not greater than 1.2(PSa), such as not greater than 1 (PSa), not greater than 0.8 (PSa), notgreater than 0.7 (PSa), not greater than 0.6 (PSa), not greater than 0.5(PSa), not greater than 0.4 (PSa), not greater than 0.3 (PSa), notgreater than 0.2 (PSa), not greater than 0.1 (PSa), not greater than0.08 (PSa), not greater than 0.06 (PSa), not greater than 0.04 (PSa),not greater than 0.03 (PSa), or even not greater than 0.02 (PSa). Still,in at least one non-limiting embodiment, the standard deviation of thespacing distance for a portion of the abrasive particles in the body canbe at least 0.0001 (PSa), such as at least 0.001 (PSa) or even at least0.01 (PSa). It will be appreciated that the standard deviation ofspacing distance can be within a range including any of the minimum andmaximum values noted above.

Reference herein to the spacing distance and standard deviation ofspacing distance can include reference to the spacing between abrasiveparticles in the same radial plane, the spacing between abrasiveparticles in different radial planes, the spacing between abrasiveparticles in the same axial collection (i.e., within the same axialplane), the spacing between abrasive particles in different axialcollections (i.e., within different axial planes), the spacing betweenabrasive particles in a radial set, the spacing between abrasiveparticles between different radial sets, the spacing between abrasiveparticles within a sector, and the spacing between abrasive particles indifferent sectors.

According to an embodiment, the abrasive particles of the first group545 can have at least one abrasive characteristic that is substantiallythe same with respect to each other. Abrasive characteristics caninclude hardness, composition, average particle size, average grainsize, fracture toughness, two-dimensional shape, tip sharpness, tipangle, aspect ratio, and a combination thereof. For example, asillustrated in FIG. 5A, the abrasive particles of the first group 545can have substantially the same two-dimensional shape (i.e., triangulartwo-dimensional shape) with respect to each other. However, it will alsobe appreciated that at least a portion of the abrasive particles withinthe first group 545 may have at least one abrasive characteristic thatis distinct from each other. Moreover, as also illustrated in 5A, theabrasive particles of the first group 545 may have at least onecharacteristic such as an orientation (e.g., a predetermined rotationalorientation) and/or predetermined position that is distinct from eachother. For example, in the illustrated embodiment of FIG. 5A, each ofthe abrasive particles 502-506 have a substantially differentpredetermined tilt angle relative to the abrasive particles 522-526. Aswill be appreciated, this need not necessarily be the case, and at leasta portion of the shaped abrasive particles of the first group, such asthe abrasive articles 502-506, can have substantially the sameorientation characteristics with respect to each other, including forexample, substantially the same predetermined tilt angle.

As further illustrated in FIG. 5A, the first group of abrasive particles545 may include a first axial set 501 of abrasive particles spaced at afirst axial distance from the major surface, such as the upper surface102 of the body 101. That is, the abrasive particles 502-506 may definea first axial set 501 of abrasive particles having substantially thesame axial distance along their respective axial axes 512-520 within thebody 101 relative to the upper surface 102. As noted herein, theabrasive particles 502-506 of the first axial set 501 can havesubstantially the same predetermined rotational orientation relative toeach other. Moreover, each of the abrasive particles 502-506 of thefirst axial set 501 can have substantially the same predeterminedrotational orientation relative to the upper surface 102 of the body101, including a predetermined three-axis orientation and apredetermined tilt angle relative to the upper surface 102 of the body101. In accordance with an embodiment, the abrasive particles 502-506 ofthe first axial set 501 may have substantially the same axial positionwith respect to each other within the body, such that they are withinthe same radial plane. Furthermore, it will be appreciated that each ofthe abrasive particles 502-506 of the first axial set 501 may have atleast one abrasive characteristic that is substantially the same withrespect to each other, including for example abrasive characteristic ofhardness, composition, average particle size, average grain size,fracture toughness, two-dimensional shape, tip sharpness, tip angle,aspect ratio, and a combination thereof.

As further illustrated, the first group of abrasive particles 545 caninclude a second axial set 521 of abrasive particles 522-526 that can bespaced at a particular axial distance from a major surface, such as theupper surface 102 of the body. That is, the abrasive particles 522-526may define a second axial set 502 of abrasive particles havingsubstantially the same axial distance along their respective axial axes512-520 within the body 101. Notably, axial distance of the abrasiveparticles 522-526 can be measured as the distance from the upper surface102 to the closest point on the particle along the respective axial axes512-520. Moreover, each of the abrasive particles 522-526 of the secondaxial set 521 may be spaced at substantially the same distance from theupper surface 102 of the body 101. Moreover, the abrasive particles522-526 of the second axial set can be spaced at a second axial distancefrom the major surface (e.g., upper surface 102) of the body that isdifferent than the first axial distance of the abrasive particles502-506 of the first axial set 501. For example, as illustrated in FIG.5A, the abrasive particles 502-506 of the first axial set 501 can bespaced at a distance closer to the upper surface 102 than the abrasiveparticles 522-526 of the second axial set 521. As provided in theillustrated embodiment, the abrasive particles 522-526 of the secondaxial set 521 are spaced further away from the upper surface 102 ascompared to the abrasive particles 502-506 of the first axial set 501.

In accordance with an embodiment, and as illustrated in FIG. 5A, theabrasive particles 522-526 can have substantially the same predeterminedrotational orientation relative to each other. For example, the abrasiveparticle 522 can have a longitudinal axis 531 that defines thepredetermined tilt angle 532 relative to the axial axis 512. Notably,the predetermined tilt angle 532 is measured at the point where thelongitudinal axis 531 is closest to the upper surface 102. Moreover, theabrasive particle 523 can have a longitudinal axis 533 that defines apredetermined tilt angle 534 relative to the axial axis 514. Theabrasive particle 524 can have a longitudinal axis 535 defining apredetermined tilt angle 536 relative to the axial axis 516. Theabrasive particle 525 can have a longitudinal axis 537 defining apredetermined tilt angle 538 relative to the axial axis 518.Furthermore, the abrasive particle 526 can have a longitudinal axis 539defining a predetermined tilt angle 540 relative to the axial axis 520.In accordance with an embodiment, each of the predetermined tilt angles532, 534, 536, 538, and 540 can be the same. Still, in an alternativeembodiment, the abrasive particles of an axial set, including forexample abrasive particles 522-526 of the second axial set 521, may havedifferent predetermined tilt angles with respect to each other.

In yet another embodiment, such as illustrated in FIG. 5A, the abrasiveparticles 502-506 of the first axial set 501 may be positioned closer tothe upper surface 102 and configured to conduct an initial materialremoval operation. The abrasive particles 522-526 of the second axialset 521 can be spaced at a greater distance from the upper surface 102than the abrasive particles 502-506 of the first axial set 501 relativeto the upper surface 102. As such, the abrasive particles 522-526 can bepositioned as backup abrasive elements configured to conduct materialremoval operations after some portion of the abrasive particles 502-506of the first axial set 501 is worn.

The abrasive particles 522-526 of the second axial set 521 can havesubstantially the same axial position with respect to each other, suchthat the abrasive particles 522-526 are positioned within the sameradial plane. Furthermore, as will be appreciated, the abrasiveparticles 522-526 of the second axial set 521 can have at least oneabrasive characteristic that is substantially the same with respect toeach other. Suitable abrasive characteristics can include, but are notlimited to, hardness, composition, average particle size, average grainsize, fracture toughness, two-dimensional shape, tip sharpness, typical,aspect ratio, and a combination thereof. Still, in at least onenon-limiting embodiment, the abrasive particles 522-526 of the secondaxial set 502 can have at least one abrasive characteristic that isdistinct from each other. Moreover, it will be appreciated that theabrasive particles 502-506 of the first axial set 501 and the abrasiveparticles 522-526 and the second axial set 521 may have at least oneabrasive characteristic that can be substantially the same with regardto each other, including for example two-dimensional shape. Still, inanother alternative embodiment, the abrasive particles 502-506 of thefirst axial set 501 may have at least one abrasive characteristic thatis distinct from the abrasive particles 522-526 of the second axial set521.

As further illustrated in FIG. 5A, at least a portion of the abrasiveparticles of the first group 545 can have a particular cutting tip orcutting edge having a predetermined orientation relative to a majorsurface, such as the upper surface 102. For example, the abrasiveparticle 502 can have a cutting tip 547 that has a particularorientation relative to the upper surface 102. Notably, the orientationof the cutting tip 547 may be defined by the predetermined tilt angle ofthe abrasive particle 502.

Referring again to FIG. 1 , in accordance with an embodiment, the body101 of the fixed abrasive article 100 can include multiple axial planes,including for example, the first axial plane 131 and the second axialplane 132. Furthermore, each axial plane may have one or more groups ofabrasive particles, including for example, the groups of abrasiveparticles 191 and 192. The groups of abrasive particles 191 and 192 canbe axial collections and/or axial sets in the respective axial planes131 and 132. Moreover, the abrasive particles of each group of abrasiveparticles 191 and 192 can have at least one abrasive characteristicand/or at least one orientation characteristic (e.g., predeterminedrotational orientation, predetermined tilt angle, predetermined verticalrotational orientation angle, and/or predetermined lateral axisrotational orientation angle) that is substantially the same withrespect to the other abrasive particles within the groups. In oneembodiment, the abrasive particles of the group of abrasive particles191 can have at least one abrasive characteristic that is substantiallythe same and/or at least one orientation characteristic (e.g.,predetermined rotational orientation, predetermined tilt angle,predetermined vertical rotational orientation angle, and/orpredetermined lateral rotational orientation) that is substantially thesame with respect to the other abrasive particles within the group 191.Still, in another embodiment, at least one abrasive particle within thegroup of abrasive particles 191 can have at least one abrasivecharacteristic and/or at least one orientation characteristic (e.g.,predetermined rotational orientation, predetermined tilt angle,predetermined vertical rotational orientation angle, and/orpredetermined lateral rotational orientation angle) that is differentcompared to at least one other abrasive particle within the group ofabrasive particles 191. For yet another embodiment, at least oneabrasive particle within the group of abrasive particles 191 can have atleast one abrasive characteristic and/or at least one orientationcharacteristic (e.g., predetermined rotational orientation,predetermined tilt angle, predetermined vertical rotational orientationangle, and/or predetermined lateral rotational orientation angle) thatis different compared to at least one other abrasive particle within thegroup of abrasive particles 192 associated with the axial plane 132.

In accordance with an embodiment, the groups of abrasive particles 191and 192 in the axial planes 131 and 132 can have any of the attributesof the abrasive particles of the group of abrasive particles 545 asdescribed in the embodiments herein. The axial plane 131 can be spacedapart from the second axial plane 132 by an angular orientation,designated as 0° and 30° respectively in the illustrated embodiment ofFIG. 1 . In certain embodiments, the abrasive particles of the groups ofabrasive particles 191 and 192 can have different axial positions,radial positions, and/or angular positions within the body 101 withrespect to each other. The abrasive particles within the groups ofabrasive particles 191 and 192 can include shaped abrasive particlesand/or elongated abrasive particles. In another embodiment, the abrasiveparticles within the groups of abrasive particles 191 and 192 can bearranged in a controlled distribution relative to each other, as viewedin their respective axial planes 131 and 132.

As further illustrated in FIG. 1 , the body 101 of the fixed abrasivearticle 100 can include multiple radial planes, including for example,the first radial plane 121 and the second radial plane 122. Furthermore,each radial plane may have one or more groups of abrasive particles,such as the groups of abrasive particles 105 and 106, which can be inthe form of radial groups and/or radial sets of abrasive particles. Inat least one embodiment, the abrasive particles of each group ofabrasive particles 105 and 106 can have at least one abrasivecharacteristic and/or at least one orientation characteristic (e.g.,predetermined rotational orientation and/or predetermined lateralrotational orientation) that is substantially the same with respect tothe other abrasive particles of the groups of abrasive particles 105 and106. In one embodiment, the abrasive particles of the group of abrasiveparticles 105 can have at least one abrasive characteristic and/or atleast one orientation characteristic (e.g., predetermined rotationalorientation and/or predetermined lateral rotational orientation) that issubstantially the same with respect to the other abrasive particleswithin the group 105. Still, in another embodiment, at least oneabrasive particle within the group of abrasive particles 105 can have atleast one abrasive characteristic and/or at least one orientationcharacteristic (e.g., predetermined rotational orientation and/orpredetermined lateral rotational orientation) that is different comparedto at least one other abrasive particle within the group of abrasiveparticles 105. For yet another embodiment, at least one abrasiveparticle within the group of abrasive particles 105 can have at leastone abrasive characteristic and/or at least one orientationcharacteristic (e.g., predetermined rotational orientation and/orpredetermined lateral rotational orientation) that is different comparedto at least one other abrasive particle within the group of abrasiveparticles 106 associated with the radial plane 121.

In accordance with an embodiment, the body 101 can include a first groupof abrasive particles 106 in the first radial plane 121 and a secondgroup of abrasive particles 105 within a second radial plane 122. Asillustrated, the first group of abrasive particles 106 in the firstradial plane 121 can be spaced apart axially from the second group ofabrasive particles 105 in the second radial plane 122 along the axialaxis 180. The groups of abrasive particles 105 and 106 within the radialplanes 121 and 122 can have any of the attributes of the abrasiveparticles described herein, including for example, the group of abrasiveparticles 545. For example, the group of abrasive particles 105 and 106can include shaped abrasive particles and/or elongated abrasiveparticles. In another embodiment, the abrasive particles within thegroups of abrasive particles 105 and 106 can be arranged in a controlleddistribution relative to each other, as viewed in their respectiveradial planes 122 and 121. As will be appreciated, the group of abrasiveparticles 105 in the second radial plane 122 can have a predeterminedposition within the radial plane 122, which can include substantiallythe same axial position within the radial plane 122 with respect to eachother. Still, in other embodiments, the abrasive particles in the secondgroup 105 can have a different radial position with respect to eachother within the radial plane 122, thus defining different radial setsof abrasive particles based on the radial positions of the abrasiveparticles. In at least one embodiment, the second group of abrasiveparticles 105 within the second radial plane 122 can have apredetermined rotational orientation relative to a major surface (e.g.,the upper surface 102) of the body 101. Moreover, the first group ofabrasive particles 106 can have a first pre-determined rotationalorientation relative to a major surface of the body 101 and the secondgroup of abrasive particles 105 can have a second predeterminedrotational orientation relative to the major surface of the body 101that may be different than the predetermined rotational orientation ofthe first group of abrasive particles 106.

The group of abrasive particles 106 in the first radial plane 121 canhave a predetermined position within the radial plane 121, and furtherhave substantially the same axial position within the radial plane 121with respect to each other. Still, in other embodiments, the abrasiveparticles in the first group 106 can have a different radial positionwith respect to each other within the radial plane 121, thus definingdifferent radial sets of abrasive particles based on the radialpositions of the abrasive particles. In at least one embodiment, thefirst group of abrasive particles 106 within the first radial plane 121can have a predetermined rotational orientation relative to a majorsurface (e.g., the upper surface 102) of the body 101.

The body 101 of the fixed abrasive article 100 can include a pluralityof groups of abrasive particles, including the first group of abrasiveparticles 106 in the radial plane 121 and second group of abrasiveparticles 105 in the radial plane 122. Moreover, each of the groups ofabrasive particles can include a plurality of radial sets of abrasiveparticles wherein each of the radial sets is spaced at different radialdistances from the center of the body 101 and the side surface 103relative to each other. For example, the first group of abrasiveparticles 106 can include a plurality of radial sets and the secondgroup of abrasive particles 105 can include a plurality of radial sets.In certain embodiments, the radial sets may establish concentric ringsof abrasive particles around the central opening 185. However, it willbe appreciated that a radial set may extend for a portion of an entirecircumference of the body 101. In at least one instance, a radial setmay extend for an entire circumference of the body at a given radialdistance from the center of the body 101.

FIG. 6 includes an illustration of a portion of a fixed abrasive articleincluding abrasive particles as viewed top-down from a major surface ofa fixed abrasive article in accordance with an embodiment. Asillustrated, and as referenced in FIG. 5A, the body 101 can includeabrasive particles 502, 503, 504, 505, and 506 (502-506) as part of thefirst group 501. Furthermore, the body can include a second group ofabrasive particles 630 including abrasive particles 631, 632, 633, and634 (631-634). In accordance with an embodiment, at least a portion ofthe abrasive particles in the body 101, including shaped abrasiveparticles and/or elongated abrasive particles, can have a predeterminedrotational orientation including a predetermined lateral axis rotationalorientation angle. For example, the abrasive particle 502 can have alateral axis 671 that defines a width of the abrasive particle 502. Thelateral axis 671, along with a normal axis 602 that extends from theparticle 502 (as viewed from a major surface of the body 101) and isnormal to the side surface 103 of the body 101, further define apredetermined lateral axis rotational orientation angle 601. A portionof abrasive particles in the body 101 may have a predetermined lateralaxis rotational orientation angle to facilitate improved materialremoval operations. In accordance with an embodiment, the portion ofabrasive particles can include the group of abrasive particles 501including abrasive particles 502-506. The abrasive particles 502-506 canbe placed within the body 101 having substantially the samepredetermined lateral axis rotational orientation angle with respect toeach other. For example, the abrasive particle 503 can have a lateralaxis 672 that, along with a normal axis 604, define a predeterminedlateral axis rotational orientation angle 603. Additionally, theabrasive particle 504 can have a lateral axis 673 that is used to definea predetermined lateral axis rotational orientation angle 605 relativeto a normal axis 606. The abrasive particle 505 can have a lateral axis674 defining a predetermined lateral axis rotational orientation angle607 relative to a normal axis 608. Moreover, the abrasive particle 506can have a lateral axis 675 defining a predetermined lateral axisrotational orientation angle 609 relative to a normal axis 610. Inaccordance with an embodiment, each of the predetermined lateral axisrotational orientation angles 601, 603, 605, 607, and 609 of theabrasive particles 502-506 can have substantially the same value. Still,in at least one embodiment, one or more of the abrasive particles502-506 of the first group 501 can have a predetermined lateral axisrotational orientation angle 601, 603, 605, 607, 609 that can bedistinct from at least one other predetermined lateral axis rotationalorientation angle within the group 501 of abrasive particles 502-506.

In accordance with an embodiment, the fixed abrasive article can beformed such that at least a portion of the abrasive particles in thebody, including shaped abrasive particles and/or elongated abrasiveparticles, can be placed within the body to have a predetermined lateralaxis rotational orientation angle of not greater than 90°, such as notgreater than 80°, not greater than 70°, not greater than 60°, notgreater than 50°, not greater than 40°, not greater than 30°, notgreater than 20°, not greater than 10°, or even not greater than 5°.Still, in another embodiment, the average predetermined lateral axisrotational orientation angle for the portion of abrasive particles canbe at least 0.1°, such as at least 1°, at least 3°, at least 5°, atleast 10°, at least 20°, at least 30°, at least 40°, or even at least50°. It will be appreciated that the portion of the abrasive particlescan have a predetermined lateral axis rotational orientation anglewithin a range including any of the minimum and maximum values notedabove. Moreover, reference to the predetermined lateral axis rotationalorientation angle for a portion of abrasive particles can includereference to an average value of the predetermined lateral axisrotational orientation angle.

In accordance with another embodiment, at least a portion of theabrasive particles within the body 101, including shaped abrasiveparticles and/or elongated abrasive particles can have a particularstandard deviation of the predetermined lateral axis rotationalorientation angle that may facilitate improved performance. For example,the portion of abrasive particles can have a standard deviation of thepredetermined lateral axis rotational orientation angle of not greaterthan 20 degrees, such as not greater than 18 degrees, not greater than16 degrees, not greater than 14 degrees, not greater than 12 degrees,not greater than 10 degrees, such as not greater than 9 degrees, notgreater than 8 degrees, not greater than 7 degrees, or even not greaterthan 6 degrees. Still, in at least one non-limiting embodiment, aportion of the abrasive particles can have a standard deviation of thepredetermined lateral axis rotational orientation angle of at least 0.1degrees, such as at least 0.5 degrees, or even at least 1 degree. Itwill be appreciated that the standard deviation of the predeterminedlateral axis rotational orientation angle can be with a range includingany of the minimum and maximum values noted above.

As further illustrated in FIG. 6 , each of the abrasive particles631-634 of the second group 630 can have a particular predeterminedlateral axis rotational orientation angle with respect to the sidesurface 103 of the body. For example, the abrasive particle 631 can havea lateral axis 681 that defines a width of the abrasive particle 631.The lateral axis 681, along with a normal axis 661 that extends from theparticle 631 (as viewed from a major surface of the body 101) and isnormal to the side surface 103 of the body 101, define a predeterminedlateral axis rotational orientation angle 641. The abrasive particle 632can have a lateral axis 682 defining a predetermined lateral axisrotational orientation angle 642 relative to the normal axis 662.Additionally, the abrasive particle 633 can have a lateral axis 683defining a predetermined lateral axis rotation orientation angle 643relative to the normal axis 663. The abrasive particle 634 can have alateral axis 684 defining a predetermined lateral axis rotationalorientation angle 644 relative to the normal axis 664. It will beappreciated that each of the abrasive particles 631-634 can have thesame attributes as the abrasive particles 502-506 of the first group501. For example, in accordance with an embodiment, each of thepredetermined lateral axis rotational orientation angles 641, 642, 643,and 644 of the abrasive particles 631-634 can have substantially thesame value. Still, in at least one embodiment, one or more of theabrasive particles 631-634 of the group 630 can have a predeterminedlateral axis rotational orientation angle 641, 642, 643, and 644 thatcan be distinct from at least one other predetermined lateral axisrotational orientation angle within the group 630 of abrasive particles631-634. As further illustrated, one or more of the abrasive particles631-634 of the group 630 can have a predetermined lateral axisrotational orientation angle 641, 642, 643, and 644 that can be distinctfrom at least one other predetermined lateral axis rotationalorientation angle within the group 501 of abrasive particles 502-506.

In accordance with an embodiment, the groups 501 and 630 of abrasiveparticles 502-506 and 631-634, respectively, can be in the same radialplane and represent a radial group of abrasive particles. According toan embodiment, groups of abrasive particles in the same radial plane canhave substantially the same axial position within the body 101 comparedto each other. Moreover, as further illustrated, the group 501 ofabrasive particles 502-506 can represent a first radial set of abrasiveparticles and the group 630 of abrasive particles 531-534 can representa second radial set of abrasive particles. The group 501 representingthe first radial set can be spaced apart radially from the group 630representing the second radial set. More particularly, in certaininstances, the first radial set of abrasive particles represented by thegroup 501 can be spaced at a different distance from the center of thebody 101 and the side surface 103 of the body 101 relative to the group630 representing the second radial set. For example, the group 501representing the first radial set can be spaced further from the centerof the body 101 and closer to the side surface 103 of the body 101relative to the second radial set represented by the group 630. Thereferenced axes 602, 604, 606, 608 and 610 can represent radial axesextending from a midpoint of the body 101 and radiating outward towardthe side surface 103 of the body 101. Moreover, the referenced axes 661,662, 663, and 664 can also represent radial axes extending from amidpoint of the body 101 and radiating outward toward the side surface103. As illustrated, each of the particles 502-506 of the group 501 havesubstantially the same radial position along their respective radialaxes 602, 604, 606, 608, and 610, and thus define a first radial set.Likewise, each of the particles 631-634 of the group 630 havesubstantially the same radial position along their respective radialaxes 661, 662, 663, and 664, and thus define a second radial set havinga different radial position relative to the abrasive particles 502-506of the first radial set. As will be appreciated, the abrasive particlesof the radial sets can have any of the attributes of other abrasiveparticles of the embodiments herein, including arrangement of theabrasive particles in controlled distributions, similarities ordifferences in abrasive characteristics, similarities or differences inpredetermined position and/or predetermined orientation and the like.

FIG. 7 includes a cross-sectional view of a portion of a body of a fixedabrasive article in accordance with an embodiment. A first axialcollection of abrasive particles 701 can include abrasive particles 702,703, 704, 705, 706, and 707 (702-707) within a first axial plane 131 ofthe body 101. The abrasive particles 702-707 can include shaped abrasiveparticles and/or elongated shaped abrasive particles. In accordance withan embodiment, each of the abrasive particles 702-707 of the first axialcollection 701 are in a predetermined position and have a substantiallystanding orientation with respect to a major surface of the body 101,such as the upper surface 102. An abrasive particle having a standingorientation includes an abrasive particle having a longitudinal axisaligned with an axial axis. For example, as illustrated, thelongitudinal axis 721 of the abrasive particle 702 extends substantiallyperpendicular to the upper surface 102 of the body 101 and substantiallyparallel to the side surface 103 of the body 101.

In accordance with an embodiment, each of the abrasive particles 702-707of the first axial collection 701 can have a predetermined rotationalorientation relative to a major surface (e.g., the upper surface 102) ofthe body 101. The predetermined rotational orientation can be defined bya predetermined tilt angle as defined in other embodiments herein. Theabrasive particles 702-707 can have the same positive, zero, or negativevalues of predetermined tilt angle as described in other embodimentsherein. Moreover, it will be appreciated that each of the abrasiveparticles 702-707 of the first axial collection 701 can havesubstantially the same predetermined rotational orientation relative toeach other. Still, in other instances, the predetermined rotationalorientation of at least two of the abrasive particles 702-707 of thefirst axial collection may be different with respect to each other.

As further illustrated in FIG. 7 , the group of abrasive particleswithin the axial plane 131 can include a second axial collection 710 ofabrasive particle 711, 712, 713, 714, 715, (711-715). The abrasiveparticles 711-715 can include shaped abrasive particles and/or elongatedshaped abrasive particles. In accordance with an embodiment, each of theabrasive particles 711-715 of the second axial collection 710 can have apredetermined position and can be in a standing orientation with respectto a major surface (e.g., an upper surface 102 and/or bottom surface104) like the abrasive particles 702-707.

The abrasive particles 711-715 can have any of the attributes of theabrasive particles 702-702 of the first axial collection 701. Forexample, each of the abrasive particles 711-715 of the second axialcollection 710 can have substantially the same predetermined rotationalorientation with respect to each other and with respect to a majorsurface of the body 101. In certain instances, the abrasive particles711-715 of the second axial collection 710 may be considered as aseparate axial set, wherein abrasive particles of the same axial set canhave substantially the same radial position and angular position withinthe body 101, but can have a different axial position in the axial plane131 relative to each other. As further illustrated, the abrasiveparticles 711-715 of the second axial collection 710 can have adifferent axial position relative to each other, such that the abrasiveparticle 711 may be closer to the upper surface 102 relative to theabrasive particle 715. Still, in certain instances, the abrasiveparticles of an axial collection, including for example abrasiveparticles 711-715, may be formed to have different radial positions withrespect to each other. For example, in certain instances the abrasiveparticles 702-707 and abrasive particle 711-715 may be part of the sameaxial collection, wherein the abrasive particle 702 can have a differentradial position relative to the abrasive particle 711. Moreparticularly, the abrasive particle 702 can be positioned at a differentradial distance from the center of the body 101 and closer to the sidesurface 103 relative to the position of the abrasive particle 711.Moreover, in certain instances, abrasive particles from two differentaxial sets can be part of the same radial group 731, such as theabrasive particle 705 from the axial set 701 and the abrasive particle713 from the axial set 710.

In addition, the abrasive particles 711-715 of the second axialcollection 710 can be arranged in a controlled distribution relative toeach other or relative to the abrasive particles 702-707 of the firstaxial collection 701. For example, the controlled distribution caninclude an ordered distribution of the abrasive particles 711-715 of thesecond axial collection 710 relative to each other. In one embodiment,the abrasive particles 711-715 of the second axial collection 710 canhave a different axial position and/or predetermined rotationalorientation compared to the abrasive particles 702-707 of the firstaxial collection 701. In another embodiment, the group of abrasiveparticles within the axial plane 131 can be in a controlled,non-shadowing arrangement. For example, two or more particles within theaxial plane 131 (e.g., particles 702, 711, 703, and 712) can beintentionally staggered relative to one another, such that each of theparticles occupies a position in a different radial plane. It has beennoted that it may be particularly advantageous to stagger the particlesrelative to each other, such that particles in the same axial plane(e.g., the group of abrasive particles within the axial plane 131) canoccupy different axial and radial positions relative to each other.Moreover, it is contemplated that abrasive particles within the sameaxial plane may be spaced at different distances relative to a majorsurface of the body 101, such that during use and wear of the abrasivearticle, new and fresh cutting tips are continuously exposed tofacilitate suitable grinding operations. Moreover, it will beappreciated that position and rotational orientation of abrasiveparticles within different groups (e.g., different radial groups) may becontrolled relative to each other.

It will be appreciated that the abrasive particles 711-715 of the axialcollection 710 can have at least one abrasive characteristic that issubstantially the same relative to each other. Suitable examples ofabrasive characteristics include hardness, composition, average particlesize, average grain size, fracture toughness, two-dimensional shape, tipsharpness, tip angle, aspect ratio, and a combination thereof. Moreover,it will be appreciated that various different abrasive particles ofdifferent axial collections may have substantially the same abrasivecharacteristic relative to each other. However, in an alternativeembodiment, different abrasive particles of different axial collectionscan have at least one abrasive characteristic that is different withrespect to each other. For example, the abrasive particles 702-707 ofthe axial collection 701 can have at least one abrasive characteristicthat is different than the abrasive particles 711-715 of the axialcollection 710.

It will be appreciated that different axial planes can include differentaxial collections of abrasive particles. For example, the axial plane131 can include a first axial collection including for example abrasiveparticles 702-707 of the first axial collection 701 and the axial plane132 may include a second axial collection separate from the first axialcollection 701, including for example, the second axial collection 710of abrasive particles 711-715.

FIG. 8 includes an illustration of a portion of a fixed abrasivearticle, as viewed in a cross-sectional plane that is parallel to anaxial plane of the article, in accordance with an embodiment. The body101 (of FIG. 1 ) can include abrasive particles 801, 802, 803, 804, and805 (801-805), which may be coupled to each other by an orientationstructure 806. It will be appreciated that at least the abrasiveparticle 805 can intersect the upper surface 102 of the body 101 and maybe at least partially protruding from the volume of the body 101 andextending axially beyond the upper surface 102. The abrasive particles801-805 may be positioned relative to the upper surface 102 andconfigured to conduct initial material removal operations using theupper surface 102 as the working surface of the abrasive article. Inaccordance with an embodiment, the orientation structure 806 can definea structure coupling at least a portion of the abrasive particles toeach other within the body 101. In certain instances, the orientationstructure 806 can be coupled to a majority of the abrasive particles,which may include shaped abrasive particles and/or elongated abrasiveparticles.

In at least one embodiment, the orientation structure 806 can be aseparate phase from the bond material 825. In accordance with anembodiment, at least a portion of the abrasive particles including, forexample, abrasive particles 801-805, may be coupled to the orientationstructure 806 that extends throughout a portion of the bond material 825within the body 101. In certain instances, the orientation structure 806can have a different composition compared to the bond material 825.Notably, the orientation structure 806 can be a material that defines aseparate phase of material from the bond material 825. In accordancewith an embodiment, the orientation structure 806 can include a materialsuch as a metal, ceramic, glass, an organic material, a polymer, and acombination thereof.

In certain instances, the orientation structure 806 may extendthroughout the entire volume of the body 101. In other instances, theorientation structure 806 may extend for at least a majority of thetotal volume of the body 801. In still another embodiment, theorientation structure 806 may extend throughout at least a portion ofthe body 801, which may be greater or less than a majority of the entirevolume of the body 101. In particular instances, the orientationstructure 806 can be coupled to the abrasive particles and configured tocontrol the three-axis position including, for example, thepredetermined position and/or predetermined rotational orientation ofthe abrasive particles within the body 101. For example, the orientationstructure 806 can be coupled to the abrasive particles 801-805 andconfigured to control the predetermined position and predeterminedrotational orientation, including the predetermined tilt angle, of theabrasive particles 801-805 relative to the upper surface 102.

For at least one embodiment, the orientation structure 806 may have aparticular hardness relative to the hardness of the bond material 825,which may facilitate certain material removal operations. For example,the orientation structure 806 can have a hardness that is less than ahardness of the bond material 825. Still, in accordance with anotherembodiment, the orientation structure 806 can have a hardness that isgreater than a hardness of the bond material 825. In yet anotherconstruction, the orientation structure 806 can have a hardness that issubstantially the same as a hardness of the bond material 825. As usedherein, substantially the same is reference to two values that arewithin 5% of each other based on the larger value.

In another embodiment, the orientation structure 806 may have aparticular hardness with respect to the abrasive particles, includingabrasive particles 801-805. For example, in at least one embodiment, theorientation structure 806 can have a hardness is less than a hardness ofthe abrasive particles 801-805. The relative hardness of the orientationstructure 806 to the abrasive particles 801-805 may be suited tofacilitate improved grinding performance Still, in certain instances,the orientation structure 806 can have a hardness that is substantiallythe same as the hardness of the abrasive particles.

The orientation structure 806 can be coupled to the abrasive particlesand configured to control the predetermined position of the abrasiveparticles within the volume of the body 101, which may include a radialposition, an axial position, and an angular position of the abrasiveparticles in the body 101. In another embodiment, the orientationstructure 806 can be coupled to each of the abrasive particles includingshaped abrasive particles and/or elongated abrasive particles throughoutthe body 101.

In accordance with another embodiment, the orientation structure 821 canbe coupled to various groups of abrasive particles including a firstgroup of abrasive particles 810, 811, 812, 813, 814, and 815 (810-815)and a second group of abrasive particles 816, 817, 818, 819, and 820(816-820). As illustrated, the first group of abrasive particles 810-815can include abrasive particles positioned in a first radial plane andthe second group of abrasive particle 816-820 can include abrasiveparticles positioned in a second radial plane. As illustrated herein,the orientation structure 821 can extend between groups of abrasiveparticles including abrasive particles 810-815 and 816-820 and bind themto each other. In accordance with an embodiment, the orientationstructure 821 can have various shapes and constructions, including forexample, a web, woven material, a nonwoven material, paper, fabric, aspun woven material, a film, a laminate, a composite, and a preformhaving regions sized and shaped to contain one or more abrasiveparticles, including a shaped abrasive particle and/or elongatedabrasive particle.

In another embodiment, the body 101 may include a first orientationstructure, such as orientation structure 806, coupled to a first groupof abrasive particles 801-805, and a second orientation structure, suchas orientation structure 821, different than the first orientationstructure 806 and coupled to the second group of abrasive particles810-820. In accordance with an embodiment, the first orientationstructure 806 can be coupled to the first group of abrasive particles801-805 positioned in a first radial plane within the body 101 and thesecond orientation structure 821 can be coupled to a second group ofabrasive particles 810-820 positioned in a second radial plane withinthe body 101. More particularly, it will be appreciated that the firstorientation structure may be coupled to a first radial set of abrasiveparticles within a radial plane and the second orientation structure canbe coupled to a second radial set of abrasive particles within a secondradial plane of the body. It will be appreciated that the first andsecond radial planes can be distinct from each other as describedherein.

In an alternative embodiment, various orientation structures may be usedand coupled to abrasive particles of different portions of abrasiveparticles within the body including, for example, different axialcollections of abrasive particles and/or different axial sets ofabrasive particles. For example, in an embodiment, a first orientationstructure may be coupled to a group of abrasive particles in a firstaxial plane associated with a first axial collection and a secondorientation structure can be coupled to a second axial collection ofabrasive particles within a second axial plane. Still, a single axialplane may utilize a plurality of orientation structures to couple one ormore axial collections of abrasive particles therein.

In a further embodiment, the abrasive particles within the axial planedepicted in FIG. 8 , namely particles 801-805, 811-815, and 816-820, canbe arranged in a controlled distribution relative to each other. Forexample, the controlled distribution can include (a) an ordereddistribution of the abrasive particles 801-805 relative to each other;(b) an ordered distribution of the abrasive particles 811-815 relativeto each other; and/or (c) an ordered distribution of the abrasiveparticles 816-820 relative to each other. In another embodiment, theabrasive particles 801-805, 811-815, and 816-820 within the axial planecan be in a controlled, non-shadowing arrangement. For example, each ofthe depicted particles in FIG. 8 can be intentionally staggered relativeto one another, such that each of the particles within the axial planeoccupies a different radial position (e.g., a different distance fromthe center of the body 101). That is, when the particles are viewed topdown in the body 101 (e.g., viewed from a plane parallel to the majorsurfaces 102 or 104), the particles in one radial plane of the body 101(e.g., the particles 801-805) do not directly overlie the particles inanother radial plane of the body 101 (e.g., either the particles 811-815or the particles 816-820). Furthermore, the particles in one radialplane of the body 101 also may have different rotational orientations(e.g., different predetermined tilt angles, different predeterminedvertical rotational orientation angles, different predetermined lateralaxis rotational orientation angles, and/or different rake angles)relative to one another or relative to the particles in another radialplane of the body 101.

FIG. 9 includes a flowchart providing a method of forming a fixedabrasive article according to an embodiment. As illustrated, the processmay be initiated at step 901 by forming a mixture including a precursorbond material. The precursor bond material can include material such asa ceramic, glass, frit, an organic material, a polymer, a resin, ametal, and a combination thereof. In certain instances, the precursorbond material may include a powder material. Still in another instance,the precursor bond material may include a liquid material. It will beappreciated that the precursor bond material may include a combinationof phases, including both solid and liquid materials, which can beprocessed later to form the finally-formed bond material of the fixedabrasive article.

As further illustrated in FIG. 9 , the process can continue at step 902by providing a forming structure configured to position abrasiveparticles in a predetermined position within the precursor bondmaterial. More particularly, FIGS. 10A-10C include illustrations of asystem for forming a fixed abrasive article according to an embodiment.FIG. 10A includes a system 1001 including a production tool 1002 inwhich the green body of the fixed abrasive article can be formed andprocessed to form the finally-formed fixed abrasive article. Inaccordance with one embodiment, the system 1001 includes a formingstructure 1006 having at least one opening 1008, in which the abrasiveparticles, such as shaped abrasive particles and/or elongated abrasiveparticles, are configured to pass through for deposition onto theprecursor bond material 1003 in a predetermined position and/orpredetermined rotational orientation. In at least one embodiment asillustrated in FIG. 10A, the abrasive particles 1007 can be deposited ina predetermined position on the precursor bond material 1003, such asthe abrasive particles 1004. As further illustrated, the formingstructure 1006 can include a container (e.g., a hopper) configured tocontain a plurality of abrasive particles 1007 and deposit them througha channel region 1009 ending in the opening 1008. The abrasive particlesmay be fed though the forming structure by gravity, vibration, or by theapplication of another force. It will be appreciated that control of thedeposition process of the abrasive particles 1004 on the precursor bondmaterial 1003 can facilitate formation of a fixed abrasive article,where the abrasive particles have a predetermined position and/orpredetermined rotational orientation.

Furthermore, the forming structure 1006 can be moved in the directions1005 and 1010 to facilitate controlled placement and orientation of theabrasive particles 1004 on the precursor bond material 1003. Inaccordance with another embodiment, the abrasive particles 1007 areconfigured to pass through the at least one opening 1008 for depositionon or within the precursor bond material 1003 with a predeterminedrotational orientation relative to a major surface of the body of thefixed abrasive article, which can be defined by a bottom surface 1031 ofthe production tool 1002. The forming structure 1006 can be configuredto move and control the predetermined position of a single abrasiveparticle by controlling the position of the forming structure 1006relative to the precursor bond material 1003. That is, the formingstructure 1006 can move in directions 1005 and 1010 and place individualabrasive particles 1004 on the precursor bond material 1003 thuscontrolling the predetermined position and/or predetermined rotationalorientation of the abrasive particles 1004 on the precursor bondmaterial 1003, and thus control the predetermined position and/orpredetermined rotational orientation of the abrasive particles 1004 inthe finally-formed abrasive article.

As further illustrated, FIG. 10B includes a second step in the formingprocess, which can include the deposition of a second layer of precursorbond material 1020 over the abrasive particles 1004. After deposition ofthe second layer of precursor bond material 1020, the process maycontinue by further deposition of abrasive particles 1007 from theforming structure 1006 on the second layer of precursor bond material1020, as illustrated in FIG. 10C. In at least one embodiment, the secondlayer of abrasive particles 1030 may be deposited in the same manner asthe abrasive particles 1004, such that they are placed on the secondlayer of precursor bond material 1020 with a predetermined positionand/or predetermined rotational orientation, which facilitates theformation of a fixed abrasive article wherein the second layer ofabrasive particles 1030 have a predetermined position and/orpredetermined rotational orientation. The abrasive particles 1004 and1030 can include shaped abrasive particles and/or elongated abrasiveparticles.

In particular instances, the process of forming the fixed abrasivearticle can include placing a first group of abrasive particles in afirst radial plane within the precursor bond material, such asillustrated in FIG. 10A, wherein the abrasive particles 1004 are placedon or overlying a first layer of precursor bond material 1003. Theprocess can further include depositing a precursor bond material overthe first group of abrasive particles 1004 in the first radial plane,such as illustrated in FIG. 10B. As will be appreciated and as furtherillustrated in FIG. 10C, the process can further include depositing asecond group of abrasive particles 1030 that may be associated with asecond radial plane overlying the first group of abrasive particles 1004the first radial plane. While reference has been made herein to thedeposition of abrasive particles in layers, such as radial planes, itwill be appreciated that the abrasive particles may be deposited ingroups, which can be associated with a group in a radial plane, a radialset, an axial collection, a portion of an axial collection, an axialset, a sector, and a combination thereof.

It will be appreciated that one or more reinforcing members may also beprovided at any point within the forming process, such as before orafter the deposition of any of the precursor bond material layers andbefore or after the deposition of any of the abrasive particles.Moreover, the forming process may include one or more processing stepsbetween the deposition of any one of the components (e.g., abrasiveparticles, layer of precursor bond material, reinforcing member,additives, etc.) used to form the fixed abrasive article. Such processescan include treatment or partial treatment of the bond material. Forexample, in at least one embodiment, the precursor bond material 1003can be cured or partially cured before the deposition of furthercomponents used to form the fixed abrasive article. Moreover, it will beappreciated that while certain abrasive particles may be deposited usingthe forming structure, further processing may be utilized for depositionof one or more other components, including for example, otherparticulate matter (e.g., diluent grains, fillers, pore formers, etc.).Deposition of the one or more other components can be conducted usingthe forming structure 1006 or a separate forming structure to controlthe predetermined position and/or predetermined rotational orientationof the one or more other components (e.g., diluent grains, fillers, poreformers, etc.). Still, in certain other instances, the process ofdeposition of the one or more other components can include deposition ofthe materials in a generally random manner.

It will be further appreciated that controlling one or more processingvariables can facilitate the formation of a fixed abrasive article wherethe abrasive particles have a predetermined position and/orpredetermined rotational orientation. For example, certain processingvariables related to the bond and the abrasive particles being used,including the composition of the precursor bond material and the averagesize of the abrasive particles, can impact the final predeterminedposition and/or predetermined rotational orientation of the abrasiveparticles within the fixed article. Certain processing conditionsrelated to curing of the green body can also contribute to the finalpositioning of the abrasive particles. For example, without wishing tobe bound by a particular theory, it is believed that by controllingcertain curing conditions (e.g., curing pressures, temperatures, andother conditions that prevent the precursor bond material from curingbefore the placement of the particles within the precursor bond materialis completed), the placement of the abrasive particles in theirpredetermined positions and/or predetermined rotational orientationsalso can be better controlled.

FIG. 11 includes a system for forming a fixed abrasive article accordingto an embodiment. As illustrated, the system 110 can include aproduction tool 1102 having a first layer of precursor bond material1103 formed therein. Additionally, a group of abrasive particles 1104have been deposited on the first layer of precursor bond material 1103.Notably, the abrasive particles 1104 which are deposited can be selectedfrom a group of abrasive particles 1112 contained in a hopper 1111.During processing, a forming structure 1106 can select a single abrasiveparticle from the group of abrasive particles 1112 at position 1110 andmove from the position 1110 to a position near the precursor bondmaterial 1103 for deposition of an abrasive particle on or within theprecursor bond material 1103 in a predetermined position and/or apredetermined rotational orientation. In accordance with an embodiment,the forming structure 1106 may be an optical pick-and-place machinecapable of rapidly selecting and controlling the predetermined positionand/or predetermined rotational orientation of a single abrasiveparticle at a time. For example, as illustrated, the forming structure1106 can be moved from position 1110 along the path 1109 with a singleabrasive particle of the group of abrasive particles 1112. The formingstructure 1106 may have complete three-space movement capabilitiesincluding, but not limited to, movement in a vertical direction 1108 andhorizontal direction 1105. The forming structure 1106 can have at leastone control head 1107 configured to hold and deposit a single abrasiveparticle. It will be appreciated that the process may employ a formingstructure having a plurality of control heads, each of which areconfigured to facilitate controlled deposition of an individual grain onor within the precursor bond material 1103 with a predetermined positionand/or a predetermined rotational orientation.

In accordance with another embodiment, a forming structure utilized tofacilitate controlled deposition of one or more abrasive particles witha predetermined position and/or predetermined rotational orientation canhave a plurality of openings. FIG. 12A includes an illustration of asystem for forming a fixed abrasive article according to an embodiment.The system 1200 includes a production tool 1202 and a forming structure1205 that can have a plurality of openings 1206 configured to allow thepassage of the abrasive particles 1204 through the openings 1206 in theforming structure 1205 for deposition of the abrasive particles 1204 onor within the precursor bond material 1203 with a predetermined positionand/or predetermined rotational orientation relative to a major surface1230 of the production tool 1202 and, ultimately, a major surface of thefinally-formed fixed abrasive article. Utilizing a forming structure1205 with a plurality of openings 1206 can facilitate rapid andsimultaneous placement of a plurality of abrasive particles 1204, suchas shaped abrasive particles and/or elongated abrasive particles, withinthe precursor bond material 1203 with a predetermined position and/orpredetermined rotational orientation.

FIG. 12B includes a top-down illustration of a forming structure 1205according to an embodiment. As illustrated, the forming structure 1205can have a plurality of openings 1221, 1222 and 1223 having variousshapes and sizes relative to each other. Moreover, as illustrated, theforming structure 1205 can have a variety of different orientations ofthe openings 1221-1223 relative to each other. It will be appreciatedthat the openings 1221-1223 may have a particular shape to control thepredetermined position and/or predetermined rotational orientation ofthe abrasive particles as the abrasive particles pass through theopenings 1221-1223. In more particular terms, for example, the openings1221 and 1223 may allow only abrasive particles having a triangulartwo-dimensional shape of a particular size range to pass through theforming structure 1205 in those particular locations, and thus controlthe predetermined position and/or predetermined rotational orientationof the abrasive particles passing therethrough on or within theprecursor bond material 1203. The openings 1222 may be sized and shapedto allow passage of certain types of abrasive particles therethroughincluding, for example, shaped abrasive particles having a rectangulartwo-dimensional shape of a particular size range.

In accordance with an embodiment, the openings 1221-1223 within theforming structure 1205 can have a particular two-dimensional shapeselected from the group consisting of a polygon, ellipsoids, irregularpolygons, Greek alphabet characters, Latin alphabet characters, Russianalphabet characters, complex shapes having a combination of polygonalshapes, shapes with a combination of linear and arcuate sections, and acombination thereof. Notably, the openings 1221-1223 can havesubstantially the same two-dimensional shape as a two-dimensional shapeof the shaped abrasive particles and/or elongated abrasive particlespassing there through. In addition, the two-dimensional shape of theopenings 1221-1223 can facilitate selective passage of only shapedabrasive particles of the desired shape and size through the openingsand thus selectively controlling the predetermined position,predetermined rotational orientation, type and size of the abrasiveparticle placed on or within the precursor bond material 1203.

Moreover, the placement of the openings 1221-1223 within the formingstructure 1205 can facilitate placement of the abrasive particles in acontrolled distribution on or within the precursor bond material 1203,and therefore, in the finally-formed fixed abrasive article. As furtherillustrated in FIG. 12C, the openings 1221-1223 can be arranged invarious configurations including a controlled distribution. Moreover, itwill be appreciated that the openings 1221-1223 can be arranged within aparticular distribution that can further define the distribution ofabrasive particles on the precursor bond material 1203. As will beappreciated, the distribution of the openings 1221-1223 can correspondto and define the controlled distribution of at least a portion of theabrasive particles within the precursor bond material 1203 and thefinally-formed fixed abrasive article. In one embodiment, the openings1221-1223 can be staggered relative to each other and relative to agiven radial axis. That is, the openings 1221-1223 can be placed inconcentric rings, but at different radial distances, from the center ofthe forming structure 1205, as is shown in FIG. 12C. At least some ofthe openings in one concentric ring (e.g., the openings 1221 positionedat one radial distance from the center of the body) also can bestaggered (not shown) relative to at least some of the openings in theother concentric rings (e.g., the openings 1222 and 1223 positioned atlesser radial distances from the center of the body). As a result, thestaggered openings 1221-1223 would occupy different positions alongdifferent radial axes of the body or be staggered in their positionsrelative to each radial axis. The abrasive particles which pass throughthe staggered openings 1221-1223 of the forming structure 1205 candefine a controlled, non-shadowing arrangement in the final fixedabrasive article.

In an alternative embodiment, the openings 1221-1223 can be blindopenings or pockets defining a space within the body of the formingstructure 1205, which do not extend completely through the thickness ofthe forming structure 1205. Still, each of the openings 1221-1223 can bearranged, sized, and shaped to contain a shaped abrasive particle and/orelongated abrasive particle and selectively control the predeterminedposition, predetermined rotational orientation, type and size of theabrasive particle placed on or within the precursor bond material 1203.Notably, in the instance where the forming structure 1205 utilizesopenings 1221-1223 in the form of pockets, the openings 1221-1223 canfirst be filled with a suitable number of shaped abrasive particlesand/or elongated abrasive particles. The forming structure 1205 can thenbe delivered to a precursor bond material 1203 and inverted such that atleast one surface of the shaped abrasive particles and/or elongatedabrasive particles contained within the openings 1221-1223 contacts asurface of the precursor bond material 1203. The forming structure 1205may then be lifted leaving the shaped abrasive particles and/orelongated abrasive particles on the precursor bond material 1203, andthe abrasive particles may have a predetermined position, predeterminedrotational orientation, and/or controlled distribution on the precursorbond material 1203 as provided by the openings 1221-1223 in the formingstructure. The single layer of a plurality of abrasive particles (e.g.,shaped abrasive particles and/or elongated abrasive particles) overlyingthe precursor bond material 1203 can define a fixed abrasive preform.One or more preforms can be made separately and then combined to form agreen body of an abrasive article. The green bond can be treatedaccording to any one of the methods herein, including for example,pressing (e.g., cold pressing, warm pressing, hot pressing, etc.) tochange the green body to a finally formed abrasive article.

Referring to FIG. 9 , the process can further include step 903, duringwhich the green body formed in step 902 is treated to form a fixedabrasive article. The process of treating can include treating theprecursor bond material to form a finally-formed bond material. Treatingmay be selected from the group of processes including, but not limitedto, heating, curing, sintering, melting, oxidizing, reducing, radiating,cooling, freezing, vibrating, pressing, and a combination thereof.Moreover, as noted herein, any of the foregoing treating processes maybe conducted completely or partially at any point during the formingprocess to facilitate the formation of a fixed abrasive article of theembodiments herein.

In an embodiment, the forming structure may be a temporary structurethat is not part of the finally-formed fixed abrasive article. Forexample, referring again to the forming structure 1205 of FIG. 12A, theforming structure 1205 may be in the form of a plate configured tocontrol the predetermined position and/or predetermined rotationalorientation of the abrasive particles as they are placed on theprecursor bond material 1203. The forming structure 1205 is removedprior to final treatment of the bond material to form the finally-formedfixed abrasive article. In such instances, the abrasive particles may betemporarily in contact with the forming structure 1205 during theforming process, but the forming structure may be removed prior to finalprocessing. In accordance with an embodiment, the forming structure 1205can include a material such as a metal, organic material, resin,polymer, glass, ceramic, monocrystalline material, polycrystallinematerial, natural material such as mineral, synthetic material, and acombination thereof.

In yet another embodiment, the forming structure can be an integratedstructure contained within the finally-formed fixed abrasive article.For example, referring to FIG. 13 , a system 1301 for forming a fixedabrasive article using a forming structure is provided in accordancewith an embodiment. The system 1301 can include a production tool 1302,a precursor bond material 1303, and abrasive particles 1304 connected toeach other via a forming structure 1305. In such instances, the formingstructure 1305 can be a permanent structure configured to connect andcouple at least a portion of the abrasive particles 1304 to each other.In such instances, the forming structure 1305 may be referred to as anorientation structure in the finally-formed fixed abrasive, wherein theabrasive particles 1304 can be permanently attached to the formingstructure 1305 and have a predetermined position and/or predeterminedrotational orientation based on their attachment to the formingstructure 1305. As such, further processing may include deposition ofprecursor bond material over the abrasive particles 1304 and formingstructure 1305 such that the forming structure 1305 is integrated withinthe finally formed fixed abrasive article.

In accordance with an embodiment, the forming structure 1305 can includea material such as a metal, an organic material, a resin, a polymer, aglass, a ceramic, a monocrystalline material, a polycrystallinematerial, a natural material such as a mineral, a synthetic material,and a combination thereof.

In one embodiment, the forming structure 1305 can be a network structureincluding abrasive particles coupled to each other. For example, theforming structure can include bridges 1305 which, in one embodiment, canbe akin to the orientation structure 821 depicted in FIG. 8 . As notedherein, in certain instances, the bridges 1305 of the forming structurecan be a permanent part of the fixed abrasive article. However, in analternative embodiment, the bridges 1305 of the forming structure may betemporary and the finally-formed fixed abrasive article can beessentially free of the bridges 1305 of the forming structure. In suchinstances, the bridges 1305 may be consumed or removed during processingto form the fixed abrasive article. For example, the bridges 1305 of theforming section connecting the abrasive particles 1304 may be removedduring treating of the green body, such as during a heating process. Forexample, one process may include volatilization of the bridges 1305,such that the bridges 1305 are evolved as a gas or form porosity withinthe finally-formed fixed abrasive article.

In other instances, the forming structure 1305, including the bridges1305 coupling the abrasive particles to each other, may be made of amaterial that is similar to the precursor bond material 1303. In someembodiments, this may facilitate absorption of at least a portion of theforming structure 1305, such as the bridges 1305, during treatment. Assuch, at least a portion of the forming structure 1305 can be integratedinto the precursor bond material and become part of the fixed abrasivearticle during the treating process. In one particular embodiment, atleast a portion of the forming structure 1305, such as the bridges 1305,can be dissociated or absorbed during treatment of the precursor bondmaterial 1303 to form the finally-formed bond material and thefinally-formed fixed abrasive article.

In yet another embodiment, the forming structure may include at leastone structure configured to allow the flow of a mixture including theprecursor bond material and abrasive particles through one or moreopenings in the forming structure to control the deposition of theprecursor bond material and abrasive particles. For example, FIG. 14Aincludes an illustration of a system for forming a fixed abrasivearticle according to an embodiment. As illustrated, the system 1401 caninclude a production tool 1402 and deposition of a precursor bondmaterial 1403 within the production tool 1402. In certain instances, thesystem may utilize multiple forming structures, including a firstforming structure 1420, which may have a reservoir for holding theprecursor bond material 1421 therein until it is deposited as a layer ofprecursor bond material 1403.

As further illustrated, a forming structure 1410 can also be utilizedand facilitate deposition of a mixture 1413 including abrasive particles1412 and precursor bond material 1411 that may be deposited through anopening of a nozzle 1431 of the forming structure 1410 in a manner tocontrol the predetermined position and/or predetermined rotationalorientation of the abrasive particles 1404. The opening of the nozzle1431 can be sized and shaped to facilitate suitable deposition of theabrasive particles 1412 and precursor bond material 1411 in the desiredmanner According to one embodiment, the mixture 1413 can be a wetmixture that is poured through at least one opening in the formingstructure 1410. In another embodiment, one or more forces may be appliedto the mixture 1413 within the forming structure 1410 to facilitatedeposition of the mixture 1413. The mixture 1413 can be deposited as alayer of precursor bond material 1405 and abrasive particles 1404,wherein the abrasive particles 1404 can have a predetermined rotationalorientation relative to a major surface of the production tool 1402 and,ultimately, the finally-formed fixed abrasive article.

The deposition of the mixture 1413 can be conducted continuously suchthat a substantially uniform layer of material is deposited. In analternative embodiment, the deposition of the mixture 1413 can be adiscontinuous process, wherein a non-uniform volume of material isdeposited over time and/or over an area to facilitate deposition of theabrasive particles 1404 in a predetermined position and/or predeterminedrotational orientation. In particular, it may be suitable that theprocess include the deposition of discrete portions 1414, which mayinclude a single abrasive particle 1404 and some content of theprecursor bond material 1405 to facilitated controlled placement of theabrasive particles in a suitable predetermined position and/orpredetermined rotational orientation.

The forming structures of the embodiments herein also can be configuredto control the predetermined tilt angle of at least a portion of theabrasive particles in the finally-formed fixed abrasive article. Assuch, the forming structure can be configured to control the averagepredetermined tilt angle and standard deviation of the predeterminedtilt angle of a portion of the abrasive particles as described inembodiments herein.

FIG. 14B includes an illustration of a system for forming a fixedabrasive article according to an embodiment. As illustrated, the system1450 can include a production tool 1402, a forming structure 1452, and adeposition structure 1451 that contains and controls deposition of amixture 1455, which mixture 1455 includes a precursor bond material 1456and abrasive particles 1457, through the forming structure 1452. Theforming structure 1452 can include openings 1454 defined betweenportions 1453. The openings 1454 can be sized and shaped to allow theflow of the mixture 1455 therethrough and orientation of the abrasiveparticles 1457 therein. The size, shape, and distribution of theopenings 1454 in the forming structure 1452 can be controlled tofacilitate a deposition of the abrasive particles 1457 with apredetermined position, a controlled distribution, and/or apredetermined rotational orientation relative to a major surface of theproduction tool 1402 and, ultimately, a major surface of thefinally-formed fixed abrasive article. While not necessarilyillustrated, it is contemplated that more than one type of formingstructure can be utilized to create different portions within the fixedabrasive article including abrasive particles of different abrasivecharacteristics and/or orientation characteristics, including but notlimited to, different predetermined positions and/or predeterminedrotational orientations. An illustration of a forming structure 1452 isshown in FIG. 14C. It will be appreciated that the forming structure1452 depicted in FIG. 14C can be employed in any of the processes orembodiments described herein, or used with any of the shaped abrasiveparticles or elongated abrasive particles described herein, to assistwith placing shaped or elongated abrasive particles in predeterminedpositions and/or predetermined rotational orientations within a fixedabrasive article.

FIG. 14C depicts a forming structure 1452 from a top-down perspective.The forming structure 1452 includes a plurality of portions, such asportions 1453, positioned within the production tool 1452. The portions1453 can be permanently affixed in any suitable configuration to theforming structure 1452 or, alternatively, can be adjusted by anysuitable means to create any suitable configuration within the formingstructure 1452. As shown in FIG. 14C, the plurality of portions 1453 arepositioned so as to be parallel with a plurality of radial axesradiating from the center of the forming structure 1452.

The plurality of portions 1453 can be positioned not only to be parallelwith radial axes radiating from the center of the forming structure1452, but each portion 1453 also is spaced apart from adjacent portions1453. In an embodiment, the average width (W) of an opening betweenadjacent portions 1453 can be selected to facilitate placement ofabrasive particles in predetermined positions and/or predeterminedrotational orientations within the final fixed abrasive article. Forexample, the average width W of the openings between adjacent portions1453 can be adjusted to correspond to a physical dimension of theabrasive particles (e.g., their average length, width, or thickness). Inan embodiment, the average width W can be controlled relative to asmallest dimension of an abrasive particle (i.e., the average width Wbetween adjacent portions 1453 can correspond to a smallest dimension ofa shaped abrasive particle or elongated abrasive particle). For example,the portions 1453 can be placed such that there is an average width Wbetween adjacent portions 1453, where the average width W correspondsto, for example, an average thickness of the shaped and/or elongatedabrasive particles. Then the mixture including the abrasive particlescan be deposited into the forming structure 1452. The portions 1453 canfacilitate not only the positioning of the abrasive particles (i.e., bypositioning the abrasive particles between the portions 1453), but alsocan facilitate the orientation of the abrasive particles, by positioningthe abrasive particles in a standing up configuration, such that thelongest dimension of the abrasive particles is substantiallyperpendicular to a major surface of the forming structure 1452 and,ultimately, a major surface of the final fixed abrasive article. In anembodiment, the average width W between adjacent portions 1453 can benot greater than the average thickness of the abrasive particles, suchas not greater than 95%, not greater than 90%, not greater than 85%, notgreater than 80%, not greater than 75%, or even not greater than 50% ofthe average thickness of the abrasive particles. In another embodiment,the average width W between adjacent portions 1453 can be not greaterthan the average width of the abrasive particles, such as not greaterthan 95%, not greater than 90%, not greater than 85%, not greater than80%, not greater than 75%, or even not greater than 50% of the averagewidth of the abrasive particles. In a further embodiment, the averagewidth W between adjacent portions 1453 can be not greater than theaverage length of the abrasive particles, such as not greater than 95%,not greater than 90%, not greater than 85%, not greater than 80%, notgreater than 75%, or even not greater than 50% of the average length ofthe abrasive particles.

FIG. 14D depicts an illustrated portion of the forming structure 1452from a top-down perspective with another configuration of the portions1453. The portions 1453 can be positioned at any suitable angle relativeto a radial axis of the forming structure 1452. For example, in FIG.14D, the portions 1453 are positioned at a 45° angle to a radial axis ofthe forming structure 1452. As discussed above, the openings betweenadjacent portions 1453 can include an average width W. That averagewidth W can correspond to a physical dimension (e.g., an average length,width, or thickness) of the abrasive particles being used in themixture. When the mixture is deposited into the forming structure 1452,the portions 1453 not only facilitate the placement of the abrasiveparticles between the portions 1453, but the portions 1453 alsofacilitate the orientation of the abrasive particles, by positioning theabrasive particles in a standing up configuration, such that the longestdimension of the abrasive particles is substantially perpendicular to amajor surface of the forming structure 1452 (and ultimately a majorsurface of the final fixed abrasive article) and a major surface of theabrasive particle is positioned at a 45° angle to a side surface of theforming structure 1452.

Furthermore, depending on the intended grinding direction of the finalfixed abrasive article, the abrasive particles being positioned at a 45°angle to a major surface of the abrasive article also can have apositive rake angle (e.g., +45° angle) or a negative rake angle (e.g.,−45° angle). For example, if the abrasive particles are positioned at a45° angle, and the angle inclines the abrasive particles in the intendedgrinding direction, then the abrasive particles have a positive rakeangle. If the abrasive particles are positioned at a 45° angle, and theangle inclines the abrasive particles opposite to the intended grindingdirection, then the abrasive particles have a negative rake angle.

FIG. 15 includes a flowchart providing a method of forming a fixedabrasive article according to an embodiment. As illustrated, the processcan be initiated at step 1501 by forming a mixture including a precursorbond material. The precursor bond material can include those materialsas noted in embodiments herein.

The process can continue at step 1502 by depositing abrasive particlesinto the precursor bond material to form a green body. As will beappreciated, the abrasive particles can include shaped abrasiveparticles and/or elongated abrasive particles as described inembodiments herein.

In accordance with at least one embodiment, the process of depositingthe abrasive particles can include forming the abrasive particles. Thatis, the abrasive particles can be formed during the process of formingthe fixed abrasive article. In one particular embodiment, the abrasiveparticles can be formed in situ during the process of forming the entirefixed abrasive article. For example, in one instance, the process caninclude forming a first portion of abrasive particles, depositing afirst portion of the precursor material on the first portion abrasiveparticles, and thereafter forming a second portion of abrasiveparticles, distinct from the first portion of abrasive particles, on thefirst portion of the precursor bond material. As will be appreciated,the first and second portions of abrasive particles can include a firstgroup in a radial plane, first and second groups in different radialplanes, a first radial set, first and second radial sets, a first axialcollection, first and second axial collections, a first axial set, firstand second axial sets, and a combination thereof. As will beappreciated, the process of forming the first portion of abrasivearticles can include forming a first portion including shaped abrasiveparticles and/or elongated abrasive particles having a predeterminedposition and/or predetermined rotational orientation relative to a majorsurface of the production tool that may define a major surface of thefinally-formed fixed abrasive article.

Certain suitable forming processes to form the abrasive particles caninclude an additive manufacturing process, printing, screen printing,shaping, casting, stamping, molding, scoring, fracturing, drying, and acombination thereof. In a particular embodiment, such as illustrated inFIG. 16 , a system 1601 for forming a fixed abrasive article accordingto an embodiment can include a production tool 1602 and a precursor bondmaterial 1603. The system 1601 further includes a deposition structure1605 such as a deposition head 1606 configured to form the abrasiveparticles 1604 in situ on the precursor bond material 1603. For example,as illustrated in FIG. 16 , discrete abrasive particles, including theabrasive particle 1607, can be formed on or within the precursor bondmaterial 1603 by the deposition structure 1605. In one embodiment, thedeposition structure 1605 can include a 3-D printing device such thatthe forming process includes 3-D printing of the abrasive particlesduring the forming of the fixed abrasive article. It will be appreciatedthat 3-D printing can include 3-D printing of shaped abrasive particlesand/or elongated abrasive particles. Moreover, while a single depositionstructure 1605 is illustrated, it is contemplated that a plurality ofdeposition structures or a single deposition structure with a pluralityof deposition heads may be utilized to simultaneously form a pluralityof abrasive particles.

The process of forming the fixed abrasive article can further includeforming abrasive particles and creating a forming structure (e.g., anorientation structure) configured to be coupled to the abrasiveparticles. As such, the forming process can include formation ofabrasive particles and one or more forming structures, which may havebridges 1612 coupling abrasive particles to each other. In certaininstances, one or more groups of abrasive particles 1604 and bridges1612 can be coupled to each other, wherein the bridges 1612 of theforming structure can facilitate holding the abrasive particles 1604 ina predetermined position and/or predetermined rotational orientationduring the forming process and within the finally-formed fixed abrasivearticle. Notably, the forming structure including the bridges 1612extending between the abrasive particles 1604 can be formed by 3-Dprinting or any of the other processes noted herein. For example, asfurther illustrated in FIG. 16 , the deposition head 1605 can include a3-D printing head configured to form the bridges 1612 of the formingstructure that extend between at least a portion of the abrasiveparticles 1604. It will be appreciated that the process of forming theabrasive particles and the forming structure together is an alternativeprocess and need not necessarily always occur.

In yet another embodiment, the process of forming the abrasive particlesduring the process of forming the fixed abrasive article can include ascreen printing process. That is, forming can include screen printingabrasive particles having a predetermined position and/or apredetermined rotational orientation on the precursor bond material.FIG. 17A includes a system of forming a fixed abrasive article accordingto an embodiment. The system 1701 can include a production tool 1702including a precursor bond material 1703 and precursor abrasiveparticles 1704 being formed within openings of a screen 1705 during ascreen printing process. As further illustrated in FIG. 17B, afterforming the precursor abrasive particles 1704 in the process of FIG.17A, the screen 1705 can be removed such that precursor abrasiveparticles 1704 are overlying the precursor bond material 1703.

The precursor abrasive particles that are formed during the process offorming the fixed abrasive article can undergo further processing toform finally-formed abrasive articles. Some suitable forming processescan include heating, curing, drying, doping, cooling, freezing, coating,sintering, and a combination thereof. In at least one embodiment, theprocess of treating the precursor shaped abrasive particles andformation of finally formed abrasive particles can be the same processthat may be used to treat the precursor bond material and form afinally-formed bond material of the finally-formed fixed abrasive.Still, in an alternative approach, the process of treating the precursorshaped abrasive particles to form final abrasive particles can be adifferent process than the process used to treat the precursor bondmaterial to form a finally-formed bond material of the finally-formedfixed abrasive.

In accordance with another embodiment, the process of depositing theabrasive particles on or within the precursor bond material can furtherinclude rearranging at least a portion of the abrasive particles to havea predetermined position and/or predetermined rotational orientation.For example, as illustrated in the process of FIG. 18 , a system 1801can include a production tool 1802 and a precursor bond material 1803formed according to an embodiment herein. As further illustrated, theabrasive particles 1804 can be deposited on the precursor bond material1803. Thereafter, the abrasive particles 1804 may be rearranged tochange the position and/or the rotational orientation of the abrasiveparticles to a predetermined position and/or predetermined rotationalorientation. In certain instances, rearranging can include providing aforce to the abrasive particles 1804, which force is configured to causea change in the predetermined position and/or rotational orientation ofthe abrasive particles 1804. For example, in one embodiment, arotational force 1805 and/or vibrational force 1805 may be applied tothe production tool 1802 to facilitate a change in the predeterminedposition and/or predetermined rotational orientation of the abrasiveparticles 1804 on or within the precursor bond material 1803. Somesuitable forces that may be utilized can include gravity, centripetal,centrifugal, uniaxial, biaxial, isometric, and a combination thereof.

Alternatively, the process of rearranging the abrasive particles caninclude providing energy to the abrasive particles configured to cause achange in the predetermined position and/or predetermined rotationalorientation of the abrasive particles on or within the precursor bondmaterial. For example, as illustrated in FIG. 18 , in certain instances,an electromagnetic energy 1806 may be applied to the abrasive particles1804 to facilitate rearranging the abrasive particles on or within theprecursor bond material 1803. The abrasive particles may include amaterial or may be coated with a material (e.g., silane) that canfacilitate their alignment by the application of electromagnetic energyand the creation of an electromagnetic field. Other suitable forms ofenergy that may be supplied to the abrasive particles 1804 can includeelectrical, mechanical, vibratory, magnetic, sonic, and a combinationthereof. While reference has been made to deposition of the abrasiveparticles and rearrangement of the abrasive particles after deposition,it will be appreciated that the process of rearrangement may beconducted during the process of deposition, such as before the abrasiveparticles 1804 contact the precursor bond material 1803.

In yet another embodiment, the process of depositing the abrasiveparticles can include deposition of a mixture of the abrasive particlesand precursor bond material into the production tool. FIG. 19 includesan illustration of a system for forming a fixed abrasive articleaccording to an embodiment. As illustrated, the system 1900 can includea production tool 1916 and a mixture 1906, including precursor bondmaterial 1903 and abrasive particles 1904. The mixture 1906 is containedin and deposited by a deposition structure 1910 through a formingstructure 1902.

In particular instances, deposition of the mixture 1906 can include oneor more processes such as printing (e.g., screen-printing), molding,pressing, casting, sectioning, cutting, dicing, punching, pressing,drying, curing, coating, extruding, rolling, and a combination thereof.In a particular embodiment, deposition includes extruding the mixture1906 through a forming structure 1902.

The forming structure 1902 can include one or more openings. The one ormore openings can be sized and shaped to allow the flow of the mixture1906 therethrough and orientation of the abrasive particles 1904therein. The size, shape, and distribution of the openings in theforming structure 1902 can be controlled to facilitate a deposition ofthe abrasive particles 1904 with a predetermined position, a controlleddistribution, and/or a predetermined rotational orientation relative toa major surface of the production tool 1916 and, ultimately, a majorsurface of the finally-formed fixed abrasive article. While notillustrated, it is contemplated that more than one type of formingstructure can be utilized to create different portions within the fixedabrasive article, where the different portions of the article includeabrasive particles of different abrasive characteristics and/ororientation characteristics including, but not limited to, predeterminedposition and/or predetermined rotational orientation.

In an embodiment, the openings in the forming structure 1902 may have atwo-dimensional shape selected from the group consisting of a polygon,an ellipsoid, a numeral, a Greek alphabet character, a Latin alphabetcharacter, a Russian alphabet character, a complex shape having acombination of polygonal shapes, and a combination thereof. In anotherembodiment, the openings in the forming structure 1902 may have a sametwo-dimensional shape as the two-dimensional shape of the abrasiveparticles 1904.

Deposition of the mixture 1906 can form a plurality of preformed bodies1914, which bodies can include abrasive particles 1904 and precursorbond material 1903, and which bodies also can have different or similarshapes and sizes. In an embodiment, all of the preformed bodies 1914 mayhave any number of same, or similar, characteristics, such as forexample, dimensions, shapes, homogeneity, or abrasive particle density.

In an embodiment, the preformed bodies 1914 may each include anelongated preformed structure. In a particular instance, each of thepreformed bodies 1914 may be in the form of a pellet or another objecthaving a predetermined shape.

The preformed bodies 1914 can each have a length (as shown by thedimension “L” in FIG. 19 ) and a maximum width, as measured in adirection perpendicular to the length and as shown by the dimension “W”in FIG. 19 . In an embodiment, the maximum width of at least one of thepreformed bodies 1914 may be a diameter of the at least one preformedbody 1914. In a particular embodiment, the length may be at least 25% ofthe maximum width, at least 100% of the maximum width, at least 150% ofthe maximum width, at least 175% of the maximum width, at least 200% ofthe maximum width, at least 250% of the maximum width, or at least 500%of the maximum width. The preformed bodies 1914 also may have an aspectratio, as measured by a ratio of the length to the width or maximumdiameter, of at least 0.1, such as at least 0.2, at least 0.5, at least1, at least 1.5, at least 2, at least 3, at least 4, at least 5, atleast 6, at least 7, at least 8, at least 9, or at least 10. In anotherembodiment, the preformed bodies 1914 may have an aspect ratio of lessthan 100, such as less than 50, or less than 25.

In certain instances, at least one of the preformed bodies 1914 may begenerally cylindrical. As used herein to describe the preformed bodies1914, “generally cylindrical” refers to a condition wherein at least oneof the preformed bodies 1914 may occupy at least 75% of a volume of abest fit cylinder, such as at least 80% of a volume of a best fitcylinder, such as at least 95% of a volume of a best fit cylinder, suchas at least 90% of a volume of a best fit cylinder, such as at least 95%of a volume of a best fit cylinder, such as at least 96% of the volumeof the best fit cylinder, at least 97% of the volume of the best fitcylinder, at least 98% of the volume of the best fit cylinder, or atleast 99% of the volume of the best fit cylinder. In a furtherembodiment, a majority of the preformed bodies 1914 may be generallycylindrical. In another embodiment, all of the preformed bodies 1914 maybe generally cylindrical. In other instances, at least one of thepreformed bodies 1914 may be cylindrical. That is, at least one of thepreformed bodies 1914 may have a first face, a second face parallel withrespect to the first face, and a cylindrical sidewall disposed betweenthe first and second faces. In a further embodiment, a majority of thepreformed bodies 1914 may be cylindrical. In another embodiment, all ofthe preformed bodies 1914 may be cylindrical.

In another embodiment, at least one of the preformed bodies 1914 mayhave a two-dimensional shape selected from the group consisting of apolygon, an ellipsoid, a numeral, a Greek alphabet character, a Latinalphabet character, a Russian alphabet character, a complex shape havinga combination of polygonal shapes, and a combination thereof.

The preformed bodies 1914 may have an abrasive particle density, asmeasured by a density of the abrasive particles 1904 relative to theoverall body of the preformed bodies 1914. In an embodiment, theabrasive particle density of the preformed bodies 1914 may be higherthan a conventional mixture of abrasive particles and precursor bondmaterial formed using a non-extrusion method or technique.

In certain instances, the abrasive particles 1904 may be homogenously,or nearly homogenously, distributed within at least one of the preformedbodies 1914. In another embodiment, the abrasive particles 1604 may berandomly or non-homogenously distributed within the preformed bodies1914.

In an embodiment, at least two of the abrasive particles 1904 disposedin at least one preformed body 1914 may have the same predeterminedthree-axis orientation with respect to one another. In anotherembodiment, at least two abrasive particles in each of the preformedbodies 1914 may have the same predetermined three-axis orientation withrespect to one another. In a further embodiment, all abrasive particlesdisposed in at least one of the preformed bodies 1914 may have the samepredetermined three-axis orientation with respect to one another. In yetanother embodiment, all abrasive particles disposed in each of thepreformed bodies 1914 may have the same predetermined three-axisorientation with respect to one another.

During or after deposition of the mixture 1906, the preformed bodies1914 may be combined, or positioned relative to one another, and treatedto form the fixed abrasive article. Additional precursor bond materialmay be applied prior to treating the preformed bodies 1914 and formingthe fixed abrasive article.

In accordance with another embodiment, the process of depositing themixture 1906 can further include rearranging at least a portion of thepreformed bodies 1914 within the production tool 1916. In an embodiment,the preformed bodies 1914 can be rearranged to abut one another. Inanother embodiment, all of the preformed bodies 1914 may be deposited ona surface of the production tool 1916 with little or no spacing betweenthe preformed bodies 1914. In a particular instance, at least two of thepreformed bodies 1914 may be deposited by the forming structure 1902 soas to be in at least partial contact with one another. In anotherparticular instance, a majority, such as all, of the preformed bodies1914 may be deposited so that each preformed body 1914 is in at leastpartial contact with an adjacent preformed body 1914.

Some reference has been made in the embodiments herein to staggering ofparticles. In addition to controlling the placement and rotationalorientation of each of the abrasive particles in the bonded abrasivebody, it may also be advantageous to control the placement androtational orientation of the abrasive particles relative to each other.For example, based upon some empirical data, it has been noted thatcertain arrangements of the abrasive particles may facilitate improvedoperations of the abrasive article. Notably, it may be advantageous tostagger the abrasive particles relative to each other and relative toone or more reference planes or axes within the body to avoid excessivewear and decreased abrasive capabilities of the abrasive article duringuse.

According to one embodiment, the abrasive particles within any plane,group, collection, or set can be arranged in a particular distributionrelative to each other. The distribution can be a pattern having shortrange order and long range order, wherein the long range order is basedon repetition of a smallest unit defining the short range order. Inanother embodiment, the distribution may be a random distribution ofabrasive particles having no discernable short range order or long rangeorder. In other instances, the distribution may be a controlled,non-uniform distribution. A controlled “non-uniform distribution” meansthat the position of the abrasive particles has a controlled asymmetry(i.e., a controlled randomness), such that although the distribution ofabrasive particles can be described by or predicted by, for example, aradial, spiral, or phyllotactic equation, the distribution of abrasiveparticles exhibits at least a partial asymmetry. The controllednon-uniform distribution can be partially, substantially, or fullyasymmetric. The controlled non-uniform distribution can be utilized fora portion of abrasive particles within any plane, group, collection,and/or set. The distribution can cover multiple portions of the abrasivearticle or can cover only a portion of the abrasive article.

It is contemplated that the controlled non-random distributionsaccording to the embodiments described herein can also include adistribution where only a portion of the total number of abrasiveparticles of the distribution possesses a controlled asymmetry. Such asituation can occur, for instance, by combining or substituting aportion of a uniformly distributed pattern or a completely randompattern with a portion of the controlled non-uniform distribution.Still, in at least one embodiment, the controlled non-randomdistribution can include a distribution where 100% of the particleshaving a controlled asymmetry.

The controlled asymmetry can be a controlled reflection asymmetry (alsocalled mirror symmetry, line symmetry, and bilateral symmetry), acontrolled rotational asymmetry, a controlled translational symmetry,controlled glide reflection symmetry, or combinations thereof. In atleast one embodiment, the non-uniform distribution can be an arrangementdescribed by a rotational asymmetry. For example, for a radial, spiral,or phyllotactic pattern having a rotational symmetry of an order of one,such a distribution has no rotational symmetry because the distributionrepeats itself only once during a rotation of 360° about its center. Inother words, if two copies of the same exact pattern are placed directlyover each other and one copy is held constant while the second copy isrotated 360° about its center, all of the apertures of both copies willcome into alignment only once during the 360° rotation.

In an embodiment, the distribution can be a phyllotactic pattern. Asused herein, “a phyllotactic pattern” means a pattern related tophyllotaxis. Phyllotaxis is the arrangement of lateral organs such asleaves, flowers, scales, florets, and seeds in many kinds of plants.Many phyllotactic patterns are marked by the naturally occurringphenomenon of conspicuous patterns having arcs, spirals, and whorls. Thepattern of seeds in the head of a sunflower is an example of thisphenomenon. Multiple arcs or spirals, also called parastichy, can havetheir origin at a center point of the distribution and travel outward,while other spirals originate to fill in the gaps left by the innerspirals. See Jean's Phyllotaxis A Systemic Study in Plant Morphogenesisat p. 17. Frequently, the spiral-patterned arrangements can be viewed asradiating outward in both the clockwise and counterclockwise directions.

FIG. 20A provides a top-down illustration of a portion of an abrasivearticle according to an embodiment. Notably, FIG. 20A includes anillustration of a radial plane 2001 within an abrasive article. Theradial plane 2001 includes shaped abrasive particles 2002 having atriangular two-dimensional shape. As illustrated, each of the abrasiveparticles is substantially standing up within the radial plane 2001.FIG. 20A is an illustration of a distribution of abrasive particleshaving a controlled, non-random distribution in the form of aphyllotactic pattern.

FIGS. 20B-D include images of other distributions that may be used tocontrol placement and rotational orientation of the abrasive particlesin a plane, group, set or collection, such that the abrasive particlesare arranged in a particular distribution within the body of theabrasive article. Each of the distributions illustrated in FIGS. 20B-Dcan represent distributions of abrasive particles that may occur in anyplane, group, set or collection within the embodiments herein. Each ofthe dots in the images of FIGS. 20B-D can represent the placement of anabrasive particle. The distributions illustrated in FIGS. 20B-D may alsorepresent a corresponding distribution of cavities for a form orproduction tool used to place the abrasive particles in the body of theabrasive article.

Moreover it will be appreciated that any of the distributionsillustrated in the figures herein can be used together or separately.For example, in one embodiment, it may be advantageous to utilize afirst type of distribution (e.g., the distribution of FIG. 25B) for afirst portion of abrasive particles (e.g., shaped abrasive particlesand/or elongated abrasive particles in a plane, group, collection orset) and a second type of distribution (e.g., the distribution of FIG.25C) for a second portion of abrasive particles (e.g., shaped abrasiveparticles and/or elongated abrasive particles in a plane, group,collection or set).

Additionally, any one of the distributions provided herein can utilizedifferent groups of abrasive particles where the abrasive particles ofone group have at least one abrasive characteristic that is differentcompared to abrasive particles of another group. For example, theabrasive article may include a distribution including a first group ofabrasive particles and a second group of abrasive particles, wherein thefirst group and second group have at least one abrasive characteristicthat is distinct from each other. Suitable examples of abrasivecharacteristics can include hardness, composition, average particlesize, average grain size, fracture toughness, two-dimensional shape, tipsharpness, tip angle, aspect ratio, or a combination thereof. Forexample, in one embodiment, a first portion of a distribution, such asthe spiral portion 2010 of FIG. 20B, can include a first type of shapedabrasive particle having a first two-dimensional shape and a secondportion of the distribution, such as the spiral portion 2011 of FIG.20B, can include a second type of abrasive particle, such as anelongated particle or a diluent particle (e.g., an unshaped abrasiveparticle). It will be appreciated that any portions of any distributionmay utilize different groups of abrasive particles where the groups haveat least one abrasive characteristic that is distinct from the abrasiveparticles in another group.

Moreover, it will be appreciated that any two portions of a distributionmay utilize abrasive particles having a different orientationcharacteristic. Exemplary orientation characteristics can include apredetermined rotational orientation, a predetermined tilt angle, apredetermined lateral axis rotational orientation, a predeterminedvertical rotational orientation, or any combination thereof. Forexample, a first portion of a distribution (e.g., the spiral portion2010) can include abrasive particles having a first predeterminedrotational orientation and a second portion of the distribution (e.g.,the spiral portion 2011) can include abrasive particles having a secondpredetermined rotational orientation that is different than the firstpredetermined rotational orientation. It will be appreciated that othercontrolled orientation characteristics may differ between differentportions of the distribution. Controlling one or more orientationcharacteristics of abrasive particles between two different portions ofa distribution may facilitate efficient grinding and limit developmentof wear flats that may affect grinding performance and life.

It will also be appreciated that one or more orientation characteristicsmay differ between particles within the same portion. As described inembodiments herein, any portion of a distribution including, forexample, the spiral portion 2010, may include different groups ofabrasive particles, which may have different abrasive characteristicsand/or orientation characteristics with respect to each other.

It will also be appreciated that different regions of the abrasivearticle, such as different axial planes, radial planes, and the like,can utilize different distributions. For example, in one embodiment, afirst radial plane of the body can include a first distribution, such asthe distribution illustrated in FIG. 20B. And a second radial plane,which can be disposed under or over the first radial plane within thebody of the abrasive article, may utilize a second distribution that isdifferent from the first distribution.

In still another embodiment, various regions within the abrasive bodymay utilize the same distribution. For example, a first radial plane anda second radial plane, which are separated from each other by some axialdistance, can utilize the same distribution, such as the distributionillustrated in FIG. 20B. In yet a more particular embodiment, it iscontemplated that the same distribution may be utilized in differentregions (e.g., radial plane) within the body of the abrasive, but thedistributions may be rotated relative to each other to facilitatesuitable staggering of the particles. For example, a first radial planemay utilize the distribution illustrated in FIG. 20B and a second radialplane overlying the first radial plane may utilize the samedistribution, but the distribution in the second radial plane is rotatedrelative to the distribution in the first radial plane, such thatabrasive particles in the same positions within the two distributionsare not overlapping, but staggered relative to each other when viewingthe radial planes top down.

In still another embodiment, a portion of the abrasive article (e.g.,such as a group of abrasive particles in the same radial plane) mayinclude a combination of abrasive particles arranged in a particulardistribution combined with other particles having a random arrangement.For example, a first group of abrasive particles, such as shapedabrasive particles, may be present in a portion of the abrasive articleincluding, for example, within the same radial plane and distributed inthe manner as illustrated in FIG. 20B. A second group of abrasiveparticles, such as diluent particles, may then be deposited at positionsbetween the positions occupied by the first group of abrasive particles,such as within the gap regions 2012 between the spiral portions 2010 and2011 that are associated with the first group of abrasive particles.Filling gap regions that exist between the positions associated with aparticular distribution may facilitate improved grinding efficiency andmay further limit the wear of the abrasive article during operation ofthe abrasive article. It will be appreciated that such an article can beformed by first depositing the first group of abrasive particles in acontrolled manner according to any of the techniques described herein,and later depositing one or more other groups of abrasive particles inthe gap regions.

FIG. 21 includes a top-down illustration of a portion of an abrasivearticle according to an embodiment. As illustrated, the abrasive article2101 includes a side surface 2102 and abrasive particles 2103, 2104,2105, 2106 and 2107 (2103-2107) contained within a first radial plane.The abrasive article further includes abrasive particles 2143, 2144,2145, 2146 and 2147 contained in a second radial plane underlying thefirst radial plane. As further illustrated, the abrasive particle 2103is spaced apart from the side surface 2102 by a spacing distance 2123,which is measured as the shortest distance along the radial axis 2113between the side surface 2102 and a point on the abrasive particle 2103closest to the side surface 2102 when viewed top down. The abrasiveparticle 2104 also includes a spacing distance 2124 along the radialaxis 2114. The abrasive particle 2105 also includes a spacing distance2125 along the radial axis 2115. The abrasive particle 2106 alsoincludes a spacing distance 2126 along the radial axis 2116. Asillustrated in FIG. 21 , the spacing distances 2123-2126 associated witheach of the abrasive particles 2103-2106 is different. This differencein spacing distances can define a staggered relationship between each ofthe adjacent abrasive particles 2103-2106 within the first radial plane,which may facilitate improved efficiency and life of the abrasivearticle.

The abrasive particles may also be staggered relative to each other indifferent radial planes. For example, as illustrated in FIG. 21 , theabrasive particle 2143, which is underlying the abrasive particle 2103can be staggered relative to the abrasive particle 2103, such that oneparticle is not completely underlying the other abrasive particle. Asillustrated in FIG. 21 , as viewed top down, at least a portion of theabrasive particle 2143 is offset from the abrasive particle 2103, suchthat the particles are not in perfect registration relative to eachother. Stated alternatively, as viewed top down, at least a portion ofthe abrasive particle 2143 is not underlying the abrasive particle 2103.Ensuring that at least a portion of the abrasive particles in differentradial planes are not in registration and have an axially and/orradially staggered relationship with respect to each other mayfacilitate improved efficiency and life of the abrasive article. It willbe appreciate that when evaluating the axial and/or radial staggering ofabrasive particles in different radial planes, such staggering is to bemeasured between the closest two particles or two immediately adjacentparticles that are separated from each other by the smallest axialdistance. FIG. 21 further illustrates the same relationship of axialstaggering for each of the pairs of abrasive particles, includingabrasive particles 2104 and 2144, abrasive particles 2105 and 2145,abrasive particles 2106 and 2146, and abrasive particles 2107 and 2147.

It will further be appreciated that the radial and/or axial staggeringof abrasive particles may be controlled by controlling one or morerotational orientation characteristics of the abrasive particles. In yetanother embodiment, the radial and/or axial staggering of abrasiveparticles may be controlled by controlling one or more rake angles ofthe abrasive particles.

Any of the foregoing methods of formation may be combined with any ofthe other methods to facilitate the formation of a fixed abrasivearticle including abrasive particles having the features of theembodiments herein. Notably, any portion of the foregoing methods can becombined with any of the features and steps of any of the otherprocesses to facilitate formation of a fixed abrasive article having thefeatures of the embodiments herein.

It will be appreciated that reference herein to any materials of thearticles of the embodiments includes forming the article essentiallyfrom any of the materials mentioned. Moreover, it will be appreciatedthat the foregoing description also contemplates that any of thearticles of the embodiments herein may be essentially free of anymaterials that are described as well as those materials that are notdescribed with any of the articles.

Many different aspects and embodiments are possible. Some of thoseaspects and embodiments are described herein. After reading thisspecification, skilled artisans will appreciate that those aspects andembodiments are only illustrative and do not limit the scope of thepresent invention. Embodiments may be in accordance with any one or moreof the items as listed below.

EMBODIMENTS

Embodiment 1. A fixed abrasive article comprising: a body havingabrasive particles contained within a bond material, the abrasiveparticles including shaped abrasive particles or elongated abrasiveparticles having an aspect ratio of length:width of at least 1.1:1,wherein a majority of the shaped abrasive particles or elongatedabrasive particles have a major axis extending substantiallynon-parallel to a major surface of the body, and wherein at least one ofthe abrasive particles is encapsulated within the bond material.

Embodiment 2. A fixed abrasive article comprising: a body havingabrasive particles contained within a bond material, the abrasiveparticles including a plurality of shaped abrasive particles orelongated abrasive particles having an aspect ratio of length:width ofat least 1.1:1, wherein the shaped abrasive particles or elongatedabrasive particles have a predetermined tilt angle, wherein the abrasiveparticles comprise a first group of abrasive particles and a secondgroup of abrasive particles, wherein abrasive particles of the firstgroup of abrasive particles have a first predetermined rotationalorientation relative to a major surface of the body, wherein abrasiveparticles of the second group of abrasive particles have a secondpredetermined rotational orientation relative to the major surface ofthe body, and wherein the first predetermined rotational orientation isdifferent from the second predetermined rotational orientation.

Embodiment 3. A fixed abrasive article comprising: a body havingabrasive particles contained within a bond material, the abrasiveparticles including a plurality of shaped abrasive particles orelongated abrasive particles having an aspect ratio of length:width ofat least 1.1:1 and opposite longitudinal ends as measured parallel tothe length, wherein at least a portion of the shaped abrasive particlesor elongated abrasive particles have a predetermined position within thebody defining a controlled distribution relative to each other, whereinthe bond material is disposed at both of the opposite longitudinal endsof at least one of the shaped abrasive particles or elongated abrasiveparticles.

Embodiment 4. The fixed abrasive article of any one of Embodiments 1, 2,and 3, wherein the bond material comprises a material selected from thegroup consisting of vitreous, polycrystalline, monocrystalline, organic,metal, and a combination thereof.

Embodiment 5. The fixed abrasive article of any one of Embodiments 1, 2,and 3, wherein the body comprises a shape selected from the groupconsisting of cylindrical, conical, cup-shaped, depressed center wheel,and a combination thereof.

Embodiment 6. The fixed abrasive article of any one of Embodiments 1, 2,and 3, wherein the body comprises a major surface including at least oneof an upper surface and a bottom surface.

Embodiment 7. The fixed abrasive article of any one of Embodiments 1, 2,and 3, wherein the body comprises a side surface extending between anupper surface and a bottom surface.

Embodiment 8. The fixed abrasive article of any one of Embodiments 1, 2,and 3, wherein the abrasive particles are contained within athree-dimensional volume of the bond material.

Embodiment 9. The fixed abrasive article of any one of Embodiments 1, 2,and 3, wherein the body comprises at least one reinforcing member,wherein the reinforcing member is selected from a group consisting of awoven material, a non-woven material, a composite material, a laminatedmaterial, a monolithic material, a natural material, a syntheticmaterial, and a combination thereof.

Embodiment 10. The fixed abrasive article of Embodiment 9, wherein thereinforcing material comprises a material selected from the groupconsisting of a monocrystalline material, a polycrystalline material, avitreous material, a glass, a ceramic, a metal, an organic material, aninorganic material, and a combination thereof, wherein the reinforcingmember

Embodiment 11. The fixed abrasive article of Embodiment 9, wherein thereinforcing material extends for at least a portion of the entire widthof the body, wherein the reinforcing material extends for a majority ofthe entire width of the body, wherein the reinforcing material extendsfor an entire width of the body.

Embodiment 12. The fixed abrasive article of Embodiment 9, wherein thereinforcing material is substantially contained within the volume of thebond material, wherein the reinforcing material is intersecting anexterior surface of the body, wherein the reinforcing material defines amajor surface of the body.

Embodiment 13. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein each of the shaped abrasive particles or elongatedabrasive particles comprise a predetermined position comprising a radialposition, an axial position, and an angular position.

Embodiment 14. The fixed abrasive article of Embodiment 13, wherein eachof the shaped abrasive particles or elongated abrasive particles furthercomprise a tilt angle relative to an axis normal to a major surface ofthe body.

Embodiment 15. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein each of the shaped abrasive particles or elongatedabrasive particles have a predetermined three-axis orientation relativeto a major surface of the body.

Embodiment 16. The fixed abrasive article of Embodiment 15, wherein atleast a portion of the shaped abrasive particles or at least a portionof the elongated abrasive particles have substantially the samepredetermined three-axis orientation relative to the major surface ofthe body.

Embodiment 17. The fixed abrasive article of Embodiment 16, wherein thepredetermined three-axis orientation includes a predetermined rotationalorientation of each the abrasive particles relative to a major surfaceof the body.

Embodiment 18. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein each of the abrasive particles comprise a cutting tipor cutting edge having a predetermined orientation relative to a majorsurface of the body.

Embodiment 19. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein the body comprises a first group of abrasive particleswithin a first radial plane within the body, each of the abrasiveparticles of the first group having a predetermined rotationalorientation within the first radial plane relative to a major surface ofthe body.

Embodiment 20. The fixed abrasive article of Embodiment 19, wherein theabrasive particles within the first group have a predetermined positionhaving substantially the same axial position within the radial planewith respect to each other.

Embodiment 21. The fixed abrasive article of Embodiment 20, wherein theabrasive particles of the first group comprise a different radialposition with respect to each other.

Embodiment 22. The fixed abrasive article of Embodiment 19, wherein thefirst group of abrasive particles includes shaped abrasive particles orelongated particles.

Embodiment 23. The fixed abrasive article of Embodiment 19, wherein theabrasive particles of the first group of abrasive particles are arrangedin a controlled distribution relative to each other.

Embodiment 24. The fixed abrasive article of Embodiment 23, wherein thecontrolled distribution includes an ordered distribution of the firstgroup of abrasive particles relative to each other within the firstradial plane.

Embodiment 25. The fixed abrasive article of Embodiment 19, wherein theabrasive particles of the first group have at least one abrasivecharacteristic that is substantially the same, wherein the at least oneabrasive characteristic is selected from the group consisting ofhardness, composition, average particle size, average grain size,fracture toughness, two-dimensional shape, tip sharpness, tip angle,aspect ratio, and a combination thereof.

Embodiment 26. The fixed abrasive article of Embodiment 19, furthercomprising a second group of abrasive particles within a second radialplane within the body, each of the abrasive particles of the secondgroup having a predetermined rotational orientation within the secondradial plane relative to the major surface of the body.

Embodiment 27. The fixed abrasive article of Embodiment 26, wherein theabrasive particles within the second group have a predetermined positionhaving substantially the same axial position within the radial planewith respect to each other.

Embodiment 28. The fixed abrasive article of Embodiment 26, wherein theabrasive particles of the second group comprise a different radialposition with respect to each other.

Embodiment 29. The fixed abrasive article of Embodiment 26, wherein thesecond group of abrasive particles include shaped abrasive particles orelongated abrasive particles.

Embodiment 30. The fixed abrasive article of Embodiment 26, wherein thesecond group of abrasive particles are arranged in a controlleddistribution relative to each other.

Embodiment 31. The fixed abrasive article of Embodiment 30, wherein thecontrolled distribution includes an ordered distribution of the secondgroup of abrasive particles relative to each other within the secondradial plane.

Embodiment 32. The fixed abrasive article of Embodiment 26, wherein thefirst radial plane and second radial plane are axially spaced apart fromeach other within the body.

Embodiment 33. The fixed abrasive article of Embodiment 26, wherein thefirst group of abrasive particles includes a first predeterminedrotational orientation and the second group of abrasive particlesincludes a second predetermined rotational orientation different thanthe first predetermined rotational orientation.

Embodiment 34. The fixed abrasive article of Embodiment 26, wherein theabrasive particles of the second group have at least one abrasivecharacteristic that is substantially the same, wherein the at least oneabrasive characteristic is selected from the group consisting ofhardness, composition, average particle size, average grain size,fracture toughness, two-dimensional shape, tip sharpness, tip angle,aspect ratio, and a combination thereof.

Embodiment 35. The fixed abrasive article of Embodiment 34, wherein theabrasive particles of the first group and the second group have at leastone abrasive characteristic that is different.

Embodiment 36. The fixed abrasive article of Embodiment 19, wherein thefirst group of abrasive particles includes a first radial set ofabrasive particles spaced at a first radial distance from a center ofthe body.

Embodiment 37. The fixed abrasive article of Embodiment 36, wherein eachof the abrasive particles of the first radial set of abrasive particleshave substantially the same predetermined rotational orientationrelative to the major surface of the body.

Embodiment 38. The fixed abrasive article of Embodiment 36, wherein eachof the abrasive particles of the first radial set of abrasive particleshave substantially the same axial position with respect to each other,and are spaced at substantially the same first radial distance from thecenter of the body with respect to each other.

Embodiment 39. The fixed abrasive article of Embodiment 36, wherein eachof the abrasive particles of the first radial set of abrasive particleshave substantially the same predetermined rotational orientationrelative to each other.

Embodiment 40. The fixed abrasive article of Embodiment 36, wherein theabrasive particles of the first radial set have at least one abrasivecharacteristic that is substantially the same, wherein the at least oneabrasive characteristic is selected from the group consisting ofhardness, composition, average particle size, average grain size,fracture toughness, two-dimensional shape, tip sharpness, tip angle,aspect ratio, and a combination thereof.

Embodiment 41. The fixed abrasive article of Embodiment 36, wherein thefirst group of abrasive particles includes a second radial set ofabrasive particles spaced at a second radial distance from a center ofthe body that is different than the first radial distance.

Embodiment 42. The fixed abrasive article of Embodiment 41, wherein eachof the abrasive particles of the second radial set of abrasive particleshave substantially the same predetermined rotational orientationrelative to each other.

Embodiment 43. The fixed abrasive article of Embodiment 41, wherein eachof the abrasive particles of the second radial set of abrasive particleshave substantially the same axial position with respect to each other,and are spaced at substantially the same second radial distance from thecenter of the body with respect to each other.

Embodiment 44. The fixed abrasive article of Embodiment 41, wherein atleast two of the abrasive particles of the second radial set of abrasiveparticles have a different predetermined rotational orientation relativeto each other.

Embodiment 45. The fixed abrasive article of Embodiment 41, wherein eachof the abrasive particles of the second radial set of abrasive particleshave substantially the same predetermined rotational orientationrelative to the major surface of the body.

Embodiment 46. The fixed abrasive article of Embodiment 41, wherein thefirst radial set is positioned as initial abrasive elements configuredto conduct initial material removal operations and the second radial setis positioned as a back-up abrasive elements configured to conductmaterial removal operations after some portion of the first radial setis worn.

Embodiment 47. The fixed abrasive article of Embodiment 41, wherein theabrasive particles of the first radial set are closer to the majorsurface of the body than the abrasive particles of the second radialset.

Embodiment 48. The fixed abrasive article of Embodiment 41, wherein theabrasive particles of the first radial set intersect the major surfaceof the body and the abrasive particles of the second radial set arespaced a distance from the major surface.

Embodiment 49. The fixed abrasive article of Embodiment 41, wherein theabrasive particles of the second radial set have at least one abrasivecharacteristic that is substantially the same, wherein the at least oneabrasive characteristic is selected from the group consisting ofhardness, composition, average particle size, average grain size,fracture toughness, two-dimensional shape, tip sharpness, tip angle,aspect ratio, and a combination thereof.

Embodiment 50. The fixed abrasive article of Embodiment 49, wherein theabrasive particles of the first radial set have at least one abrasivecharacteristic different than the abrasive particles of the secondradial set.

Embodiment 51. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein the body comprises a plurality of groups of abrasiveparticles associated with a plurality of different radial planes withinthe body, and wherein each group of the plurality of groups of abrasiveparticles includes a plurality of radial sets of abrasive particles,wherein each of the radial sets are spaced at a different radialdistance from a center of the body relative to each other.

Embodiment 52. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein the body comprises a plurality of axial collections ofabrasive particles, wherein each axial collection includes a pluralityof abrasive particles contained within a same axial plane within thebody.

Embodiment 53. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein the body comprises a first axial collection ofabrasive particles within a first axial plane within the body, each ofthe abrasive particles of the first axial collection having apredetermined rotational orientation relative to a major surface of thebody.

Embodiment 54. The fixed abrasive article of Embodiment 53, wherein theabrasive particles of the first axial collection have a predeterminedposition including substantially the same axial position and angularposition within the body.

Embodiment 55. The fixed abrasive article of Embodiment 54, wherein theabrasive particles of the first axial collection have a different radialposition with respect to each other.

Embodiment 56. The fixed abrasive article of Embodiment 53, wherein theabrasive particles of the first axial collection include shaped abrasiveparticles or elongated abrasive particles.

Embodiment 57. The fixed abrasive article of Embodiment 53, wherein theabrasive particles of the first axial collection of abrasive particlesare arranged in a controlled distribution relative to each other.

Embodiment 58. The fixed abrasive article of Embodiment 57, wherein thecontrolled distribution includes an ordered distribution of the firstaxial collection of abrasive particles relative to each other within thefirst axial plane.

Embodiment 59. The fixed abrasive article of Embodiment 53, wherein theabrasive particles of the first axial collection have at least oneabrasive characteristic that is substantially the same, wherein the atleast one abrasive characteristic is selected from the group consistingof hardness, composition, average particle size, average grain size,fracture toughness, two-dimensional shape, tip sharpness, tip angle,aspect ratio, and a combination thereof.

Embodiment 60. The fixed abrasive article of Embodiment 53, furthercomprising a second axial collection of abrasive particles within asecond axial plane within the body that is different than the firstaxial plane, each of the abrasive particles of the second axialcollection having a predetermined rotational orientation within thesecond axial plane relative to the major surface of the body.

Embodiment 61. The fixed abrasive article of Embodiment 60, wherein theabrasive particles of the second axial collection have a predeterminedposition including substantially the same axial position and angularposition within the body.

Embodiment 62. The fixed abrasive article of Embodiment 60, wherein theabrasive particles of the second axial collection have a differentradial position with respect to each other.

Embodiment 63. The fixed abrasive article of Embodiment 60, wherein theabrasive particles of the second axial collection include shapedabrasive particles or elongated abrasive particles.

Embodiment 64. The fixed abrasive article of Embodiment 60, wherein thesecond axial collection of abrasive particles are arranged in acontrolled distribution relative to each other.

Embodiment 65. The fixed abrasive article of Embodiment 64, wherein thecontrolled distribution includes an ordered distribution of the secondaxial collection of abrasive particles relative to each other within thesecond axial plane.

Embodiment 66. The fixed abrasive article of Embodiment 60, wherein theabrasive particles of the second axial collection have at least oneabrasive characteristic that is substantially the same, wherein the atleast one abrasive characteristic is selected from the group consistingof hardness, composition, average particle size, average grain size,fracture toughness, two-dimensional shape, tip sharpness, tip angle,aspect ratio, and a combination thereof.

Embodiment 67. The fixed abrasive article of Embodiment 66, wherein theabrasive particles of the first axial collection have at least oneabrasive characteristic different than the abrasive particles of thesecond axial collection.

Embodiment 68. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein each of the shaped abrasive particles or elongatedabrasive particles have a predetermined tilt angle defining an anglebetween a normal axis extending normal to the major surface of the bodyand a longitudinal axis of the shaped abrasive particle or elongatedabrasive particle.

Embodiment 69. The fixed abrasive article of Embodiment 68, wherein thetilt angle is 0 degrees.

Embodiment 70. The fixed abrasive article of Embodiment 68, wherein thetilt angle is greater than 0 degrees at least 2 degrees or at least 4degrees or at least 6 degrees or at least 8 degree or at least 10degrees or at least 15 degrees or at least 20 degrees or at least 25degrees or at least 30 degrees or at least 35 degree or at least 45degrees or at least 50 degrees or at least 55 degrees or at least 60degrees or at least 65 degrees or at least 70 degree or at least 75degrees or at least 80 degrees.

Embodiment 71. The fixed abrasive article of Embodiment 70, wherein thetilt angle is not greater than 90 degrees or not greater than 88 degreesor not greater than 85 degrees or not greater than 80 degrees or notgreater than 75 degrees or not greater than 70 degrees or not greaterthan 65 degrees or not greater than 60 degrees or not greater than 55degrees or not greater than 50 degrees or not greater than 45 degrees ornot greater than 40 degrees or not greater than 35 degrees or notgreater than 30 degrees or not greater than 25 degrees or not greaterthan 20 degrees or not greater than 15 degrees or not greater than 10degrees or not greater than 8 degrees or not greater than 6 degrees.

Embodiment 72. The fixed abrasive article of Embodiment 68, wherein thebody includes a first portion of shaped abrasive particles or elongatedabrasive particles having a tilt angle variation of not greater than 20degrees with respect to each other or not greater than 10 degrees or notgreater than 8 degrees or not greater than 6 degrees or not greater than5 degrees or not greater than 4 degrees or not greater than 3 degrees ornot greater than 2 degrees, wherein the first group of shaped abrasiveparticles or elongated abrasive particles have substantially the sametilt angle with respect to each other.

Embodiment 73. The fixed abrasive article of Embodiment 72, wherein thefirst portion includes at least one of a first group, a first radialset, a first axial collection, and a combination thereof.

Embodiment 74. The fixed abrasive article of Embodiment 72, wherein thefirst portion includes at least a majority of the shaped abrasiveparticles or a majority of the elongated abrasive particles in the body.

Embodiment 75. The fixed abrasive article of Embodiment 72, wherein thefirst portion includes essentially all of the shaped abrasive particlesor essentially all of the elongated abrasive particles in the body.

Embodiment 76. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein each of the shaped abrasive particles or elongatedabrasive particles have a predetermined tilt angle defining an anglebetween a radial axis and a particle axis, wherein the predeterminedtilt angle is within a range between 0 degrees and 90 degrees.

Embodiment 77. The fixed abrasive article of Embodiment 76, furthercomprising an average predetermined tilt angle for the shaped abrasiveparticles or elongated abrasive particles of not greater than 90 degreesor not greater than 80 degrees or not greater than 70 degrees or notgreater than 60 degrees or not greater than 50 degrees or not greaterthan 40 degrees or not greater than 30 degrees or not greater than 20degrees or not greater than 10 degrees or not greater than 5 degrees.

Embodiment 78. The fixed abrasive article of Embodiment 76, furthercomprising an average predetermined tilt angle for the shaped abrasiveparticles or elongated abrasive particles of at least 0.1 degrees or atleast 1 degree or at least 3 degrees or at least 5 degree or at least 10degrees or at least 20 degrees or at least 30 degrees or at least 40degree or at least 50 degrees.

Embodiment 79. The fixed abrasive article of Embodiment 76, furthercomprises a standard deviation of predetermined tilt angle of notgreater than 20 degrees or not greater than 10 degrees or not greaterthan 9 degrees or not greater than 8 degrees or not greater than 7degrees or not greater than 6 degrees.

Embodiment 80. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein at least a portion of the abrasive particles arecoupled to an orientation structure extending throughout a portion ofthe bond material within the body.

Embodiment 81. The fixed abrasive article of Embodiment 80, wherein theorientation structure has a different composition compared to the bondmaterial.

Embodiment 82. The fixed abrasive article of Embodiment 80, wherein theorientation structure defines a structure coupling at least a portion ofthe abrasive particles to one another and defining a separate phase fromthe bond material.

Embodiment 83. The fixed abrasive article of Embodiment 80, wherein theorientation structure is coupled to a majority of the shaped abrasiveparticles or elongated abrasive particles.

Embodiment 84. The fixed abrasive article of Embodiment 80, wherein theorientation structure comprises a material selected from the groupconsisting of a metal, a ceramic, a glass, an organic material, apolymer, and a combination thereof.

Embodiment 85. The fixed abrasive article of Embodiment 80, wherein theorientation structure extends throughout an entire volume of the body.

Embodiment 86. The fixed abrasive article of Embodiment 80, wherein theorientation structure extends throughout at least a portion of theentire volume of the body, wherein the orientation structure extendsthroughout a majority of the entire volume of the body.

Embodiment 87. The fixed abrasive article of Embodiment 80, wherein theorientation structure is coupled to the abrasive particles andconfigured to control a predetermined rotational orientation of theabrasive particles within the body.

Embodiment 88. The fixed abrasive article of Embodiment 80, wherein theorientation structure is coupled to the abrasive particles andconfigured to control a predetermined position including a radialposition, an axial position, and an angular position of the abrasiveparticles within the body.

Embodiment 89. The fixed abrasive article of Embodiment 80, wherein theorientation structure is coupled to each of the shaped abrasiveparticles or elongated abrasive particles throughout the body.

Embodiment 90. The fixed abrasive article of Embodiment 80, wherein theorientation structure comprises a hardness less than a hardness of thebond material.

Embodiment 91. The fixed abrasive article of Embodiment 80, wherein theorientation structure comprises a hardness less than a hardness of theabrasive particles.

Embodiment 92. The fixed abrasive article of Embodiment 80, wherein theorientation structure comprises a hardness greater than a hardness ofthe bond material.

Embodiment 93. The fixed abrasive article of Embodiment 80, wherein theorientation structure comprises a hardness substantially the same as ahardness of the bond material.

Embodiment 94. The fixed abrasive article of Embodiment 80, wherein theorientation structure comprises a hardness substantially the same as ahardness of the abrasive particles.

Embodiment 95. The fixed abrasive article of Embodiment 80, wherein theorientation structure comprises a web, a woven material, a non-wovenmaterial, paper, fabric, a spunwoven material, a film, a laminate, acomposite, a preform with regions sized to contain a shaped abrasiveparticle or elongated abrasive particle, and a combination thereof.

Embodiment 96. The fixed abrasive article of Embodiment 80, wherein thebody comprises a first orientation structure associated with a firstgroup of abrasive particles and a second orientation structure differentthan the first orientation structure associated with a second group ofabrasive particles.

Embodiment 97. The fixed abrasive article of Embodiment 96, wherein thefirst orientation structure is associated with a first group of abrasiveparticles within a first radial plane and the second orientationstructure is associated with a second group of abrasive particles withina second radial plane.

Embodiment 98. The fixed abrasive article of Embodiment 96, wherein thefirst orientation structure is associated with a first radial set ofabrasive particles within a first radial plane and the secondorientation structure is associated with a second radial set of abrasiveparticles.

Embodiment 99. The fixed abrasive article of Embodiment 96, wherein thefirst orientation structure is associated with a first axial collectionof abrasive particles within a first axial plane and the secondorientation structure is associated with a second axial collection ofabrasive particles within a second axial plane.

Embodiment 100. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein the abrasive particles comprise a material selectedfrom the group consisting of oxides, carbides, nitrides, borides,oxycarbides, oxynitrides, oxyborides, diamond, carbon-containingmaterials, and a combination thereof, or wherein the abrasive particlescomprise a monocrystalline material, polycrystalline material, avitreous material, and a combination thereof, or wherein the abrasiveparticles comprise at least one material selected from the groupconsisting of alumina, zirconia, magnesia, rare-earth oxides, and acombination thereof.

Embodiment 101. The fixed abrasive article of Embodiment 100, whereinthe abrasive particles further comprise particles selected from thegroup consisting of diluent particles, agglomerated particles, naturalparticles, synthetic particles, and a combination thereof.

Embodiment 102. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein the shaped abrasive particles comprise a materialselected from the group consisting of oxides, carbides, nitrides,borides, oxycarbides, oxynitrides, oxyborides, diamond,carbon-containing materials, and a combination thereof, or wherein theshaped abrasive particles comprise a monocrystalline material,polycrystalline material, a vitreous material, and a combinationthereof, or wherein the shaped abrasive particles comprise at least onematerial selected from the group consisting of alumina, zirconia,magnesia, rare-earth oxides, and a combination thereof.

Embodiment 103. The fixed abrasive article of Embodiment 102, whereineach of the shaped abrasive particles have a body including at leastabout 95 wt % alumina for the total weight of the body.

Embodiment 104. The fixed abrasive article of Embodiment 102, whereineach of the shaped abrasive particles have a body including not greaterthan about 99.5 wt % alumina for the total weight of the body.

Embodiment 105. The fixed abrasive article of Embodiment 102, whereineach of the shaped abrasive particles have a body comprising apolycrystalline material including crystalline grains, wherein theaverage grain size is not greater than about 1 micron.

Embodiment 106. The fixed abrasive article of Embodiment 102, whereineach of the shaped abrasive particles have a body comprising apolycrystalline material including crystalline grains, wherein theaverage grain size is at least about 0.01 microns.

Embodiment 107. The fixed abrasive article of Embodiment 102, whereineach of the shaped abrasive particles have a body that is essentiallyfree of a binder, or wherein the body is essentially free of an organicmaterial, or wherein the body is essentially free of rare earthelements, or wherein the body is essentially free of iron, or whereinthe body is formed from a seeded sol gel.

Embodiment 108. The fixed abrasive article of Embodiment 102, each ofthe shaped abrasive particles have a body comprising a two-dimensionalshape as viewed in a plane defined by a length and a width of the bodyselected from the group consisting of polygons, ellipsoids, numerals,Greek alphabet characters, Latin alphabet characters, Russian alphabetcharacters, complex shapes having a combination of polygonal shapes, anda combination thereof.

Embodiment 109. The fixed abrasive article of Embodiment 102, whereineach of the shaped abrasive particles have a body comprising atriangular two-dimensional shape.

Embodiment 110. The fixed abrasive article of Embodiment 102, whereineach of the shaped abrasive particles have a body comprising athree-pointed star two-dimensional shape.

Embodiment 111. The fixed abrasive article of Embodiment 102, whereineach of the shaped abrasive particles have a body, and the bodycomprises at least one tip having a tip sharpness of not greater than 80microns or not greater than 70 microns or not greater than 60 microns ornot greater than 50 microns.

Embodiment 112. The fixed abrasive article of Embodiment 111, whereinthe tip comprises a tip sharpness of at least 1 micron.

Embodiment 113. The fixed abrasive article of Embodiment 102, whereineach of the shaped abrasive particles have a body comprising a length(1), a width (w), and a height (hi), wherein the length≥width, thelength≥height, and the width≥height.

Embodiment 114. The fixed abrasive article of Embodiment 113, whereinthe height (h) is at least about 100 microns the width not greater thanabout 5 mm and the length not greater than 5 mm

Embodiment 115. The fixed abrasive article of Embodiment 113, whereinthe body comprises a primary aspect ratio of length:width of at leastabout 1:1 and not greater than about 10:1.

Embodiment 116. The fixed abrasive article of Embodiment 113, whereinthe body comprises a secondary aspect ratio defined by a ratio ofwidth:height within a range between about 5:1 and about 1:1.

Embodiment 117. The fixed abrasive article of Embodiment 113, whereinthe body comprises a tertiary aspect ratio defined by a ratio oflength:height within a range between about 6:1 and about 1:1.

Embodiment 118. The fixed abrasive article of Embodiment 113, whereinthe body comprises a dishing value (d) of not greater than about 2 ornot greater than about 1.5 or not greater than about 1.2.

Embodiment 119. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein the body further comprises an additive selected fromthe group consisting of fillers, grinding aids, pore inducers, hollowmaterials, catalysts, coupling agents, curants, anti-static agents,suspending agents, anti-loading agents, lubricants, wetting agents,dyes, fillers, viscosity modifiers, dispersants, defoamers, and acombination thereof.

Embodiment 120. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein the body comprises a major surface configured toconduct a material removal operation.

Embodiment 121. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein the body comprises a porosity within a range including0.5 vol % and 80 vol % for a total volume of the body.

Embodiment 122. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein the body comprises a content of abrasive particleswithin a range including at least 0.5 vol % and not greater than 50 vol% for a total volume of the body.

Embodiment 123. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein the body comprises a content of bond material within arange including at least 0.5 vol % and not greater than 50 vol % for atotal volume of the body.

Embodiment 124. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein the body is in the form of a thin wheel having a ratioof diameter:thickness of at least 10:1 or at least 50:1 or at least100:1.

Embodiment 125. The fixed abrasive article of Embodiment 124 wherein thebody comprises a thickness of not greater than 10 mm

Embodiment 126. The fixed abrasive article of Embodiment 124 wherein thebody comprises a diameter of at least 20 mm

Embodiment 127. A method of forming a fixed abrasive article comprising:forming a mixture including a precursor bond material; providing aforming structure configured to position abrasive particles comprisingshaped abrasive particles or elongated abrasive particles each having anaspect ratio of length:width of at least 1.1:1, in a predeterminedposition within the precursor bond material; and treating the green bodyto form a fixed abrasive article having a body and wherein each of theabrasive particles have a predetermined position within the body or apredetermined rotational orientation relative to a major surface of thebody.

Embodiment 128. The method of Embodiment 127, wherein the precursor bondmaterial comprises a material selected from the group consisting of aceramic, a glass, a frit, an organic material, a polymer, a metal, and acombination thereof.

Embodiment 129. The method of Embodiment 127, wherein the precursor bondmaterial includes a powder.

Embodiment 130. The method of Embodiment 127, further comprisingtreating the green body to form a fixed abrasive article having a bodyand wherein each of the abrasive particles have a predetermined positionwithin the body and a predetermined rotational orientation relative to amajor surface of the body.

Embodiment 131. The method of Embodiment 127, wherein the formingstructure comprises at least one opening and the abrasive particles areconfigured to pass through the at least one opening for deposition inthe precursor bond material in a predetermined position.

Embodiment 132. The method of Embodiment 131, wherein the abrasiveparticles are configured to pass through the at least one opening fordeposition in a predetermined position within the body of the fixedabrasive article.

Embodiment 133. The method of Embodiment 131, wherein the abrasiveparticles are configured to pass through the at least one opening fordeposition in the precursor bond material in a predetermined rotationalorientation relative to a major surface of the body of the fixedabrasive article.

Embodiment 134. The method of Embodiment 131, wherein the formingstructure is configured to move and control the predetermined positionof a single abrasive particle by controlling the position of the formingstructure relative to the precursor bond material.

Embodiment 135. The method of Embodiment 131, wherein the formingstructure is configured to place a single abrasive particle at a timeonto the precursor bond material to control the predetermined positionof each of the abrasive particles.

Embodiment 136. The method of Embodiment 127, further comprisingtreating the green body to form a fixed abrasive article having a bodyand wherein each of the shaped abrasive particles or elongated abrasiveparticles have a predetermined position within the body.

Embodiment 137. The method of Embodiment 127, wherein the formingstructure comprises openings.

Embodiment 138. The method of Embodiment 137, further comprising passingthe abrasive particles through the openings in the forming structure fordeposition of the abrasive particles into the precursor bond material inthe predetermined position.

Embodiment 139. The method of Embodiment 138, wherein passing theabrasive particles through the openings in the forming structureincludes passing an abrasive particle through an opening in the formingstructure to place the abrasive particle in the precursor bond materialwith a predetermined rotational orientation with respect to a majorsurface of the body.

Embodiment 140. The method of Embodiment 137, wherein the openings arepositioned on the forming structure to control the position of each ofthe abrasive particles within the precursor bond material.

Embodiment 141. The method of Embodiment 137, wherein the openings havea shape configured to control the rotational orientation of the abrasiveparticles as the abrasive particles pass through the openings.

Embodiment 142. The method of Embodiment 137, wherein the openings havea two-dimensional shape selected from the group consisting of a polygon,an ellipsoid, a numeral, a Greek alphabet character, a Latin alphabetcharacter, a Russian alphabet character, a complex shape having acombination of polygonal shapes, and a combination thereof.

Embodiment 143. The method of Embodiment 137, wherein the openings havesubstantially the same two-dimensional shape as the two-dimensionalshape of the shaped abrasive particles or elongated abrasive particles.

Embodiment 144. The method of Embodiment 137, wherein the openings arearranged in a distribution within the forming structure.

Embodiment 145. The method of Embodiment 144, wherein the distributionof the openings corresponds to the distribution of at least a portion ofthe abrasive particles within the body.

Embodiment 146. The method of Embodiment 127, wherein the processincludes placing a first group of abrasive particles in a first radialplane within the precursor bond material.

Embodiment 147. The method of Embodiment 146, wherein the processincludes placing a first group of shaped abrasive particles or elongatedparticles in a first radial plane within the precursor bond material.

Embodiment 148. The method of Embodiment 146, wherein the first group ofabrasive particles is a layer of the abrasive particles overlying alayer of precursor bond material.

Embodiment 149. The method of Embodiment 146, further comprisingdepositing precursor bond material over the first group of abrasiveparticles in the first radial plane.

Embodiment 150. The method of Embodiment 149, further comprisingdepositing a second group of abrasive particles in a second radial planeoverlying the first group of abrasive particles in the first radialplane.

Embodiment 151. The method of Embodiment 150, further comprisingdepositing a second group of shaped abrasive particles or elongatedabrasive particles in a second radial plane overlying the first group ofabrasive particles in the first radial plane.

Embodiment 152. The method of Embodiment 150, wherein the second groupof abrasive particles is a layer of abrasive particles overlying a layerof precursor bond material and the layer of the first group of abrasiveparticles.

Embodiment 153. The method of Embodiment 150, wherein depositing thesecond group of abrasive particles includes depositing the second groupof abrasive particles on a layer of the precursor bond material disposedbetween the first group of abrasive particles and the second group ofabrasive particles.

Embodiment 154. The method of Embodiment 150, further comprisingtreating the precursor bond material to form a bond material

Embodiment 155. The method of Embodiment 127, wherein the formingstructure is temporary structure that is not included within the fixedabrasive article.

Embodiment 156. The method of Embodiment 127, wherein the formingstructure is an integrated structure contained within the fixed abrasivearticle.

Embodiment 157. The method of Embodiment 127, wherein the abrasiveparticles are permanently attached to the forming structure.

Embodiment 158. The method of Embodiment 127, wherein the abrasiveparticles are temporarily in contact with the forming structure.

Embodiment 159. The method of Embodiment 127, wherein the formingstructure is a template configured to control the predetermined positionof the abrasive particles.

Embodiment 160. The method of Embodiment 127, wherein the formingstructure is a template configured to control a predetermined rotationalorientation of the abrasive particles relative to a major surface of thebody of the fixed abrasive article.

Embodiment 161. The method of Embodiment 127, wherein the formingstructure is a network structure including the abrasive particlescoupled to each other by bridges.

Embodiment 162. The method of Embodiment 161, wherein the bridges arepermanent and a part of the fixed abrasive article.

Embodiment 163. The method of Embodiment 161, wherein the bridges aretemporary and the fixed abrasive article is essentially free of thebridges.

Embodiment 164. The method of Embodiment 161, wherein the bridges areconsumed or removed during processing to form the fixed abrasivearticle.

Embodiment 165. The method of Embodiment 161, wherein the bridges areremoved during treating of the green body.

Embodiment 166. The method of Embodiment 127, wherein the mixturecomprises the precursor bond material and abrasive particles includingshaped abrasive particles or elongated abrasive particles, wherein themixture is translated through the forming structure to form a layer ofprecursor bond material and abrasive particles having a predeterminedrotational orientation relative to a major surface of the layer.

Embodiment 167. The method of Embodiment 166, wherein the mixture is awet mixture and the mixture is poured through openings in the formingstructure to form a layer of precursor bond material and abrasiveparticles having a predetermined rotational orientation relative to amajor surface of the layer.

Embodiment 168. The method of Embodiment 127, wherein the formingstructure is selected from a group of materials consisting of a metal,organic, resin, polymer, glass, ceramic, monocrystalline,polycrystalline, natural material, synthetic material, and a combinationthereof.

Embodiment 169. The method of Embodiment 127, wherein the formingstructure is configured to control a predetermined tilt angle of theabrasive particles.

Embodiment 170. The method of Embodiment 169, wherein the tilt angle is0 degrees.

Embodiment 171. The method of Embodiment 169, wherein the tilt angle isgreater than 0 degrees at least 2 degrees or at least 4 degrees or atleast 6 degrees or at least 8 degree or at least 10 degrees or at least15 degrees or at least 20 degrees or at least 25 degrees or at least 30degrees or at least 35 degree or at least 45 degrees or at least 50degrees or at least 55 degrees or at least 60 degrees or at least 65degrees or at least 70 degree or at least 75 degrees or at least 80degrees.

Embodiment 172. The method of Embodiment 169, wherein the tilt angle isnot greater than 90 degrees or not greater than 88 degrees or notgreater than 85 degrees or not greater than 80 degrees or not greaterthan 75 degrees or not greater than 70 degrees or not greater than 65degrees or not greater than 60 degrees or not greater than 55 degrees ornot greater than 50 degrees or not greater than 45 degrees or notgreater than 40 degrees or not greater than 35 degrees or not greaterthan 30 degrees or not greater than 25 degrees or not greater than 20degrees or not greater than 15 degrees or not greater than 10 degrees ornot greater than 8 degrees or not greater than 6 degrees.

Embodiment 173. The method of Embodiment 169, further comprising a tiltangle variation of the abrasive particles of not greater than 10 degreeswith respect to each other or not greater than 8 degrees or not greaterthan 6 degrees or not greater than 5 degrees or not greater than 4degrees or not greater than 3 degrees or not greater than 2 degrees.

Embodiment 174. The method of any one of Embodiments 132-173, whereinproviding the forming structure configured to position abrasiveparticles further comprises: depositing the abrasive particles and theprecursor bond material to form a preformed body.

Embodiment 175. The method of Embodiment 174, wherein depositing theabrasive particles and the precursor bond material comprises extrusion.

Embodiment 176. The method of any one of Embodiments 132-175, whereinproviding the forming structure configured to position abrasiveparticles further comprises: forming a mixture comprising the abrasiveparticles and the precursor bond material; and extruding the mixturethrough the forming structure to form a preformed body including theabrasive particles and the precursor bond material.

Embodiment 177. The method of any one of Embodiments 175 and 176,wherein the preformed body comprises a plurality of preformed bodies,wherein the plurality of preformed bodies are combined to form the fixedabrasive article.

Embodiment 178. The method of any one of Embodiments 132-177, whereinproviding the forming structure configured to position abrasiveparticles is performed so as to form a plurality of elongated preformedstructures.

Embodiment 179. The method of any one of Embodiments 132-178, whereinproviding the forming structure configured to position abrasiveparticles is performed so as to form a plurality of preformed bodies.

Embodiment 180. The method of Embodiment 179, wherein the preformedbodies have a length and a maximum width, as measured in a directionperpendicular to the length, and wherein the length is greater than themaximum width, wherein the length is at least 150% the maximum width, atleast 175% the maximum width, at least 200% the maximum width, at least250% the maximum width.

Embodiment 181. The method of any one of Embodiments 179 and 180,wherein the preformed bodies have an aspect ratio as measured by a ratioof length to a maximum width, as measured in a direction perpendicularto the length, and wherein the aspect ratio is at least 1.5, at least 2,at least 3, at least 4, at least 5, at least 6, at least 7, at least 8,at least 9, at least 10.

Embodiment 182. The method of any one of Embodiments 179-181, whereinthe preformed bodies have an aspect ratio as measured by a ratio oflength to a maximum width, as measured in a direction perpendicular tothe length, and wherein the aspect ratio is less than 100, less than 50,less than 25.

Embodiment 183. The method of any one of Embodiments 179-182, wherein atleast one of the preformed bodies is generally cylindrical, wherein atleast one of the preformed bodies is cylindrical, wherein a majority ofthe preformed bodies are generally cylindrical, wherein a majority ofthe preformed bodies are cylindrical, wherein all of the preformedbodies are generally cylindrical, wherein all of the preformed bodiesare cylindrical.

Embodiment 184. The method of any one of Embodiments 179-183, whereinthe preformed bodies have first and second faces oriented parallel withrespect to each other and a cylindrical sidewall disposed between thefirst and second faces.

Embodiment 185. The method of any one of Embodiments 179-184, whereinthe preformed bodies have an abrasive particle density, and wherein theabrasive particle density is higher than a mixture formed using anon-extruded method.

Embodiment 186. The method of any one of Embodiments 181-185, wherein atleast two abrasive particles disposed in at least one of the preformedbodies have a same predetermined three-axis orientation with respect toone another, wherein at least two abrasive particles disposed in each ofthe preformed bodies have a same predetermined three-axis orientationwith respect to one another, wherein all abrasive particles disposed inat least one of the preformed bodies have a same predeterminedthree-axis orientation with respect to one another, wherein all abrasiveparticles disposed in each of the or preformed bodies have a samepredetermined three-axis orientation with respect to one another.

Embodiment 187. A method of forming a fixed abrasive article comprising:forming a mixture including a precursor bond material; depositingabrasive particles comprising shaped abrasive particles or elongatedabrasive particles each having an aspect ratio of length:width of atleast 1.1:1 into the precursor bond material; and treating the greenbody to form a fixed abrasive article having a body and abrasiveparticles contained in the body in a predetermined position or apredetermined rotational orientation relative to a major surface of thebody.

Embodiment 188. The method of Embodiment 187, wherein depositingincludes forming the abrasive particles.

Embodiment 189. The method of Embodiment 188, wherein forming of theabrasive particles is conducted during the process of forming the fixedabrasive article.

Embodiment 190. The method of Embodiment 189, wherein forming comprises:forming a first portion of abrasive particles; depositing a firstportion of a precursor bond material on the first portion of abrasiveparticles; and forming a second portion of abrasive particles distinctfrom the first portion of abrasive particles on the first portion of theprecursor bond material.

Embodiment 191. The method of Embodiment 190, wherein the first portionincludes at least one of a first group, a first radial set, a firstaxial collection, and a combination thereof.

Embodiment 192. The method of Embodiment 190, wherein the second portionincludes at least one of a second group, a second radial set, a secondaxial collection, and a combination thereof.

Embodiment 193. The method of Embodiment 190, wherein forming the firstportion includes forming a first portion of shaped abrasive particles orelongated abrasive particles having a predetermined position or apredetermined rotational orientation relative to a major surface of thebody.

Embodiment 194. The method of Embodiment 190, wherein forming the firstportion includes forming a first portion of shaped abrasive particles orelongated abrasive particles having a predetermined position and apredetermined rotational orientation relative to a major surface of thebody.

Embodiment 195. The method of Embodiment 188, wherein forming comprisesa process selected from the group consisting of additive manufacturing,printing, shaping, casting, stamping, molding, and a combinationthereof.

Embodiment 196. The method of Embodiment 195, wherein forming comprisesscreen printing of the abrasive particles.

Embodiment 197. The method of Embodiment 195, wherein forming comprisesscreen printing of the shaped abrasive particles or elongated abrasiveparticles.

Embodiment 198. The method of Embodiment 196, wherein forming comprises3D printing of the abrasive particles.

Embodiment 199. The method of Embodiment 195, wherein forming comprises3D printing of the shaped abrasive particles or elongated abrasiveparticles.

Embodiment 200. The method of Embodiment 187, wherein depositingincludes forming a forming structure including abrasive particles.

Embodiment 201. The method of Embodiment 200, wherein the formingstructure comprises abrasive particles coupled to each other by bridges.

Embodiment 202. The method of Embodiment 195, wherein the formingstructure is formed by 3D printing.

Embodiment 203. The method of Embodiment 195, wherein the formingstructure is configured to control the predetermined position of theabrasive particles.

Embodiment 204. The method of Embodiment 195, wherein the formingstructure is configured control a predetermined rotational orientationof the abrasive particles relative to a major surface of the body.

Embodiment 205. The method of Embodiment 187, further comprisingtreating the green body to form a fixed abrasive article having a bodyand abrasive particles contained in the body in a predetermined positionand a predetermined rotational orientation relative to a major surfaceof the body

Embodiment 206. The method of Embodiment 187, further comprisingrearranging at least a first portion of the abrasive particles to have apredetermined rotational orientation.

Embodiment 207. The method of Embodiment 206, wherein the precursor bondmaterial is partially treated prior to rearranging.

Embodiment 208. The method of Embodiment 206, wherein treating iscompleted after rearranging.

Embodiment 209. The method of Embodiment 206, wherein rearrangingincludes changing the rotational orientation of the abrasive particlesfrom a random rotational orientation to a predetermined rotationalorientation.

Embodiment 210. The method of Embodiment 206, wherein rearrangingincludes changing the predetermined rotational orientation of theabrasive particles within the precursor bond material.

Embodiment 211. The method of Embodiment 206, wherein rearrangingincludes changing the predetermined rotational orientation of the firstportion of the abrasive particles to have a standard deviation of apredetermined tilt angle of not greater than 10 or not greater than 9 ornot greater than 8 or not greater than 7 or not greater than 6.

Embodiment 212. The method of Embodiment 211, wherein the first portionincludes at least one of a first group, a first radial set, a firstaxial collection, and a combination thereof.

Embodiment 213. The method of Embodiment 206, wherein rearrangingincludes changing a predetermined tilt angle of the first portion of theabrasive particles.

Embodiment 214. The method of Embodiment 213, wherein changing thepredetermined tilt angle includes changing the predetermined tilt angleof the first portion of the abrasive particles to have a predeterminedtilt angle variation of not greater than 10 degrees with respect to eachother or not greater than 8 degrees or not greater than 6 degrees or notgreater than 5 degrees or not greater than 4 degrees or not greater than3 degrees or not greater than 2 degrees.

Embodiment 215. The method of Embodiment 213, wherein the first portionincludes at least one of a first group, a first radial set, a firstaxial collection, and a combination thereof.

Embodiment 216. The method of Embodiment 206, wherein rearrangingincludes providing energy to the abrasive particles configured to causea change in the rotational orientation of the abrasive particles.

Embodiment 217. The method of Embodiment 216, wherein the energy isselected from the group consisting of electrical, mechanical, vibratory,electromagnetic, magnetic, sonic, and a combination thereof.

Embodiment 218. The method of Embodiment 206, wherein rearrangingincludes providing a force to the abrasive particles configured to causea change in the rotational orientation of the abrasive particles.

Embodiment 219. The method of Embodiment 218, wherein the force isselected from the group consisting of gravity, centrifical, centrifugal,uniaxial, biaxial, isometric, and a combination thereof.

Embodiment 220. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein the body is essentially free of a fixation layer.

Embodiment 221. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein the body is substantially uniform compositionthroughout a volume of the body, wherein the body has a substantiallyhomogenous composition throughout a volume of the body.

Embodiment 222. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein a majority of the abrasive particles are encapsulatedwithin the bond material, wherein all of the abrasive particles areencapsulated within the bond material.

Embodiment 223. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein at least 1% of the abrasive particles are encapsulatedwithin the bond material, wherein at least 5% of the abrasive particlesare encapsulated within the bond material, wherein at least 10% of theabrasive particles are encapsulated within the bond material, wherein atleast 25% of the abrasive particles are encapsulated within the bondmaterial, wherein at least 50% of the abrasive particles areencapsulated within the bond material, wherein at least 75% of theabrasive particles are encapsulated within the bond material, wherein atleast 90% of the abrasive particles are encapsulated within the bondmaterial, wherein at least 95% of the abrasive particles areencapsulated within the bond material.

Embodiment 224. The fixed abrasive article of any one of Embodiments 1,2, and 3, wherein at least one of the abrasive particles is encapsulatedin a material having a uniform composition, wherein a majority of theabrasive particles are encapsulated within the material having a uniformcomposition, wherein all of the abrasive particles are encapsulatedwithin the material having a uniform composition.

Embodiment 225. A method of forming a fixed abrasive article comprising:forming a mixture including a precursor bond material; providing aforming structure configured to position abrasive particles comprisingshaped abrasive particles or elongated abrasive particles each having anaspect ratio of length:width of at least 1.1:1, in a predeterminedposition within the precursor bond material; passing the precursor bondmaterial and abrasive particles through the forming structure to form aplurality of preformed bodies; treating the plurality of preformedbodies to form a fixed abrasive article having a body, wherein each ofthe abrasive particles have a predetermined position within the body ora predetermined three-axis orientation.

Embodiment 226. The method of Embodiment 225, wherein the precursor bondmaterial comprises a material selected from the group consisting of aceramic, a glass, a frit, an organic material, a polymer, a metal, and acombination thereof.

Embodiment 227. The method of Embodiment 225, wherein the precursor bondmaterial includes a powder.

Embodiment 228. The method of Embodiment 225, further comprisingtreating the preformed bodies to form a fixed abrasive article having abody, wherein at least a majority of the abrasive particles have apredetermined position within the body and a predetermined three-axisorientation.

Embodiment 229. The method of Embodiment 225, wherein the formingstructure comprises at least one opening and the abrasive particles areconfigured to pass through the at least one opening for deposition inthe precursor bond material in a predetermined position or apredetermined three-axis orientation.

Embodiment 230. The method of Embodiment 225, wherein passing theabrasive particles through the forming structure comprises extruding theprecursor bond material and abrasive particles through an opening in theforming structure.

Embodiment 231. The method of Embodiment 230, wherein the formingstructure is adapted to control the position of each of the abrasiveparticles within the precursor bond material.

Embodiment 232. The method of Embodiment 230, wherein the opening has ashape configured to control the rotational orientation of the abrasiveparticles.

Embodiment 233. The method of Embodiment 230, wherein the opening has atwo-dimensional shape selected from the group consisting of a polygon,an ellipsoid, a numeral, a Greek alphabet character, a Latin alphabetcharacter, a Russian alphabet character, a complex shape having acombination of polygonal shapes, and a combination thereof.

Embodiment 234. The method of Embodiment 230, wherein the opening hassubstantially the same two-dimensional shape as the two-dimensionalshape of the shaped abrasive particles or elongated abrasive particles.

Embodiment 235. The method of Embodiment 230, wherein the formingstructure comprises a plurality of openings.

Embodiment 236. The method of Embodiment 225, wherein the abrasiveparticles are homogeneously distributed throughout each of the preformedbodies.

Embodiment 237. The method of Embodiment 225, wherein the formingstructure is a temporary structure that is not included within the fixedabrasive article.

Embodiment 238. The method of Embodiment 225, wherein the formingstructure is an integrated structure contained within the fixed abrasivearticle.

Embodiment 239. The method of Embodiment 225, wherein the abrasiveparticles are permanently attached to the forming structure.

Embodiment 240. The method of Embodiment 225, wherein the abrasiveparticles are temporarily in contact with the forming structure.

Embodiment 241. The method of Embodiment 225, wherein the formingstructure is a template configured to control the predetermined positionof the abrasive particles.

Embodiment 242. The method of Embodiment 225, wherein the formingstructure is a network structure including the abrasive particlescoupled to each other by bridges.

Embodiment 243. The method of Embodiment 225, wherein the mixturecomprises the precursor bond material and abrasive particles includingshaped abrasive particles or elongated abrasive particles, wherein themixture is translated through the forming structure to form a pluralityof elongated particles, and wherein the abrasive particles have apredetermined rotational orientation relative to a major surface of theelongated particles.

Embodiment 244. The method of Embodiment 225, wherein the mixture is awet mixture and the mixture is poured through openings in the formingstructure.

Embodiment 245. The method of Embodiment 225, wherein the formingstructure is selected from a group of materials consisting of a metal,organic, resin, polymer, glass, ceramic, monocrystalline,polycrystalline, natural material, synthetic material, and a combinationthereof.

Embodiment 246. The method of Embodiment 225, wherein the formingstructure is configured to control a predetermined tilt angle of theabrasive particles.

Embodiment 247. The method of Embodiment 246, wherein the tilt angle is0 degrees.

Embodiment 248. The method of Embodiment 246, wherein the tilt angle isgreater than 0 degrees at least 2 degrees or at least 4 degrees or atleast 6 degrees or at least 8 degree or at least 10 degrees or at least15 degrees or at least 20 degrees or at least 25 degrees or at least 30degrees or at least 35 degree or at least 45 degrees or at least 50degrees or at least 55 degrees or at least 60 degrees or at least 65degrees or at least 70 degree or at least 75 degrees or at least 80degrees.

Embodiment 249. The method of Embodiment 246, wherein the tilt angle isnot greater than 90 degrees or not greater than 88 degrees or notgreater than 85 degrees or not greater than 80 degrees or not greaterthan 75 degrees or not greater than 70 degrees or not greater than 65degrees or not greater than 60 degrees or not greater than 55 degrees ornot greater than 50 degrees or not greater than 45 degrees or notgreater than 40 degrees or not greater than 35 degrees or not greaterthan 30 degrees or not greater than 25 degrees or not greater than 20degrees or not greater than 15 degrees or not greater than 10 degrees ornot greater than 8 degrees or not greater than 6 degrees.

Embodiment 250. The method of Embodiment 246, further comprising a tiltangle variation of the abrasive particles of not greater than 10 degreeswith respect to each other or not greater than 8 degrees or not greaterthan 6 degrees or not greater than 5 degrees or not greater than 4degrees or not greater than 3 degrees or not greater than 2 degrees.

The above-disclosed subject matter is to be considered illustrative, andnot restrictive, and the appended claims are intended to cover all suchmodifications, enhancements, and other embodiments, which fall withinthe true scope of the present invention. Thus, to the maximum extentallowed by law, the scope of the present invention is to be determinedby the broadest permissible interpretation of the following claims andtheir equivalents, and shall not be restricted or limited by theforegoing detailed description.

The Abstract of the Disclosure is provided to comply with Patent Law andis submitted with the understanding that it will not be used tointerpret or limit the scope or meaning of the claims. In addition, inthe foregoing Detailed Description, various features may be groupedtogether or described in a single embodiment for the purpose ofstreamlining the disclosure. This disclosure is not to be interpreted asreflecting an intention that the claimed embodiments require morefeatures than are expressly recited in each claim. Rather, as thefollowing claims reflect, inventive subject matter may be directed toless than all features of any of the disclosed embodiments. Thus, thefollowing claims are incorporated into the Detailed Description, witheach claim standing on its own as defining separately claimed subjectmatter.

What is claimed is:
 1. A fixed abrasive article comprising: a bodyincluding elongated abrasive particles contained within a bond material,wherein each of the elongated abrasive particles comprise an aspectratio of length:width of at least 1.1:1, and wherein at least a portionof the elongated abrasive particles are coupled to an orientationstructure embedded within the bond material, and wherein the orientationstructure comprises a hardness that is greater than a hardness of thebond material, and a hardness that is less than the hardness of theportion of elongated abrasive particles coupled to the orientationstructure.
 2. The fixed abrasive article of claim 1, wherein theelongated abrasive particles include shaped abrasive particles, whereineach of the shaped abrasive particles comprise a body defined by alength, width, and thickness, and wherein each body comprises atwo-dimensional shape as defined by a plane of the length and width, thetwo-dimensional shape selected from the group consisting of polygons,ellipsoids, numerals, Greek alphabet characters, Latin alphabetcharacters, Russian alphabet characters, complex shapes having acombination of polygonal shapes, and a combination thereof.
 3. The fixedabrasive article of claim 1, wherein the orientation structure includesa material comprising a metal, ceramic, glass, an organic material, apolymer, and a combination thereof.
 4. The fixed abrasive article ofclaim 1, wherein the orientation structure includes a material thatdefines a separate phase from the bond material.
 5. The fixed abrasivearticle of claim 1, wherein the orientation structure extends throughoutat least a portion of the body of the fixed abrasive article.
 6. Thefixed abrasive article of claim 1, wherein the orientation structureextends throughout the entire volume of the body of the fixed abrasivearticle.
 7. The fixed abrasive article of claim 1, wherein the fixedabrasive article comprises a coated abrasive article or a bondedabrasive article.
 8. The fixed abrasive article of claim 1, wherein theorientation structure is configured to control at least one of apredetermined position and a predetermined rotational orientation of theelongated abrasive particles within the body of the fixed abrasivearticle.
 9. The fixed abrasive article of claim 1, wherein the elongatedabrasive particles include shaped abrasive particles and the orientationstructure is configured to control a predetermined position and apredetermined rotational orientation of the shaped abrasive particleswithin the body of the fixed abrasive article.
 10. The fixed abrasivearticle of claim 1, wherein the portion of elongated abrasive articlesare coupled to the orientation structure and coupled to each other viathe orientation structure, and wherein the portion of elongated abrasiveparticles intersect an upper surface of the body and are partiallyprotruding from the volume of the body of the fixed abrasive article.11. The fixed abrasive article of claim 1, wherein the orientationstructure comprises a ceramic.
 12. The fixed abrasive article of claim1, wherein the orientation structure is configured to control thethree-axis position of the portion of elongated abrasive particlesattached to the orientation structure.
 13. The fixed abrasive article ofclaim 1, wherein the orientation structure is configured to control apredetermined tilt angle of the shaped abrasive particles relative to anupper surface of the fixed abrasive article.
 14. The fixed abrasivearticle of claim 1, wherein the orientation structure is configured tocontrol a predetermined position of the shaped abrasive particles withinthe volume of the body including a radial position, an axial position,and an angular position of the abrasive particles in the body.
 15. Thefixed abrasive article of claim 1, wherein the orientation structurecomprises a hardness that is greater than a hardness of the bondmaterial.
 16. The fixed abrasive article of claim 1, wherein theorientation structure comprises a hardness that is substantially thesame as the hardness of the bond material.
 17. The fixed abrasivearticle of claim 1, wherein the orientation structure comprises ahardness that is substantially the same as the hardness of the elongatedabrasive particles coupled to the orientation structure, and wherein theorientation structure comprises a hardness that is greater than ahardness of the bond material.
 18. The fixed abrasive article of claim1, wherein the orientation structure is constructed from a preformhaving regions sized and shaped to contain one or more shaped abrasiveparticles.
 19. The fixed abrasive article of claim 1, wherein theorientation structure is a first orientation structure and the portionof elongated abrasive particles is a first group of abrasive particle,and wherein the fixed abrasive article comprises a second orientationstructure different than the first orientation structure and including asecond group of abrasive particles coupled to the second orientationstructure.
 20. The fixed abrasive article of claim 1, wherein theportion of elongated abrasive particles are arranged in a controlleddistribution relative to each other.